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Computational Studies ofProtein Aggregation: Methodsand ApplicationsAlex Morriss-Andrews1 and Joan-Emma Shea1,21Department of Physics and 2Department of Chemistry, University of California, Santa Barbara,California 93106; email: [email protected]

Annu. Rev. Phys. Chem. 2015. 66:64366

The Annual Review of Physical Chemistry is online atphyschem.annualreviews.org

This articles doi:10.1146/annurev-physchem-040513-103738

Copyright c 2015 by Annual Reviews.All rights reserved

Keywords

amyloid brils, coarse-grained models, molecular dynamics simulations,replica exchange molecular dynamics, enhanced sampling methods,systematic coarse graining

Abstract

Protein aggregation involves the self-assembly of normally soluble proteinsinto large supramolecular assemblies.The typical end product of aggregationis the amyloid bril, an extended structure enriched in -sheet content. Theaggregation process has been linked to a number of diseases, most notablyAlzheimers disease, but bril formation can also play a functional role incertain organisms.This review focuses on theoretical studies of the process ofbril formation, with an emphasis on the computationalmodels andmethodscommonly used to tackle this problem.

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Review in Advance first posted online on January 30, 2015. (Changes may still occur before final publication online and in print.)

Changes may still occur before final publication online and in print

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1. BACKGROUND

The computational study of protein aggregation has established itself as a mature and proliceld of research, with over 10,000 publications, dating back to the 1970s. The eld, however, hasrecently burgeoned, propelled by greater computational resources, the application of enhancedsampling algorithms, and the development of novel coarse-grained models. This review focuseson these latest developments. We begin with an overview of protein aggregation, followed bya description of computational models and methodologies, with a few selected applications asillustrations.

Proteins are polymers of amino acids, synthesized on ribosomes and released as extendedchains. A class known as globular proteins folds to a specic three-dimensional structure, eitheron their own or with the help of chaperone molecules. This folded state corresponds to the bio-logically active, functional state. Other proteins are intrinsically disordered and only populate afunctional state once bound to a partner molecule. Proteins exist in a crowded, heterogeneous cel-lular environment that can dramatically affect folding and association between proteins. Changesin cellular condition (pH, temperature) or changes in the protein (mutation, posttranslationalmodication, overexpression) can lead to misfolding or partial unfolding of a protein and subse-quent self-assembly into aggregate structures (1). The aggregation process is often considered apathological one that depletes active proteins, and the formation of potentially toxic aggregatespecies can indeed be harmful to the cell. Several diseases, including Alzheimers, Parkinsons,and some forms of cancer, are closely linked to protein aggregation (2). Yet it is noteworthy thataggregation is not problematic in all instances: Several organisms use it for functional purposes(e.g., biolms in bacteria) (3).

The common end product of aggregation, seen in both pathological and physiological aggre-gation processes, is the extended amyloid bril (100 nm long), highly enriched in content,with a cross- structure. The latter involves an arrangement of sheets running parallel to thebril axis, with perpendicular hydrogen bonds (4, 5) (see Figure 1).

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Figure 1(a) Twisted morphology of a TTR(105115) bril. (b) Close-up view showing the molecular detail. Figure adapted from Reference 4,with images created using the following structures: Electron Microscopy Data Bank, EMDB accession number EMD-2324, andProtein Data Bank, http://www.pdb.org (PDB ID code 2m5n).

644 Morriss-Andrews Shea


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Nucleation

Partiallyunfolded

monomer

Nativestate

Smalloligomers

Nucleus

Protofibrils

Maturefibrils

Time

Agg

rega

tion

Growth

Elongation ordissociation at

fibril end Fragmentation

Secondarynucleation

Association

Figure 2Schematic illustration of the bril nucleation growth mechanism, including secondary nucleation andfragmentation processes.

Experimental studies of protein aggregation indicate a sigmoidal trace for the kinetics of brilformation, as shown schematically in Figure 2. This sigmoidal shape has traditionally been as-cribed to a standard nucleation growth mechanism, in which a partially folded monomer associateswith others to form a critical nucleus (the nucleation phase), at which point a small bril emergesand elongates (the growth phase). The primary growth process is often attributed to bril-endelongation by a dock-lockmechanism, in which themonomer rst binds to the edge of the growingbril (the dock phase) and then rearranges its structure once bound (the lock phase). The processis more complex in reality, with the formation of not only a host of on- and off-pathway oligomers,but also secondary processes such as lateral growth, fragmentation, and association (69).

Protein aggregation is an attractive eld to theorists because theoretical and computationalchallenges are coupled to a problem of real biological importance. The process of aggregationinvolves length scales of one to hundreds of nanometers and timescales that can exceed hours(Figure 3). As a result, the study of protein aggregation lends itself to a hierarchy of models, fromthe quantum mechanical to the mesoscopic (Figure 4). This review focuses primarily on classicalmolecular dynamics studies of atomistic and coarse-grained models (Figure 5).

2. ATOMISTIC MODELS

Atomistic models of both the protein and solvent offer the most detail but come at a large com-putational cost. They are used primarily to study monomeric and very small oligomeric com-plexes, as well as the stability of preformed bril models and their interaction with dyes or smallmolecule or peptide inhibitors. Typically, the study of monomers and small oligomers needs to

www.annualreviews.org Computational Studies of Protein Aggregation 645


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1 ns

1 ps

1 s

1 ms1 s

1 min

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1 year

Loop closure

Helixformation

Proteinaggregation

Proteinfolding

Folding of hairpins

Side-chainrotations

PHE

Figure 3Illustration showing the contrasting breadth of timescales of protein rearrangement and assembly, from fastside-chain rotations to slow protein aggregation.

be augmented by enhanced sampling methods, such as the replica exchange molecular dynamics(REMD) and metadynamics methods described in Section 4.2. The convergence of simulationsis often problematic, with small proteins of 20 amino acids requiring on the order of severalhundred nanoseconds per replica (27).

Atomistic simulations have provided important insights into the structure of the early stagesof aggregation, at a resolution that surpasses experimental capabilities. The initial partially foldedaggregate-prone structure and prenucleus assemblies are transient, unstable species, difcult todetect experimentally. Simulations have been particularly instrumental for the case of intrinsicallydisordered peptides, capturing the transient secondary structure, which may provide clues aboutthe protein regions responsible for initiating aggregation. Not only have simulations been ableto study protein fragments, they also are now at the stage at which they can tackle full-lengthproteins implicated in amyloid diseases, including the 4042-residue-long amyloid- (A) peptidelinked to Alzheimers disease and the islet amyloid polypeptide (IAPP) associated with type IIdiabetes.

A powerful approach combines molecular dynamics simulations (typically with the replicaexchange sampling protocol described in Section 4.2) with nuclear magnetic resonance (NMR)(molecular dynamics/NMR methodology). With this approach, important new information hasbeen obtained regarding structural differences arising at the monomeric level between the A40and A42 alloforms. Experiments have shown that these peptides, which differ uniquely by the



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ps ns s ms s

nm

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Time

Leng

th

QM model

Atomistic model

Coarse-grained model

Continuum model

Figure 4The approximate timescales involved in different classes of molecular simulations: quantum mechanical(QM) (10), atomistic (1114), coarse-grained (1517), and continuum models (18).

presence of two additional residues at the C terminus of the peptide, aggregate via different path-ways (28, 29). Simulations were instrumental in complementing experimental studies by showingthat, although the peptides were considered intrinsically disordered, populating an ensemble ofdiverse conformations, regions of local secondary structure could be identied (25, 30). In par-ticular, simulations by Garcia and coworkers (25) demonstrated that both A40 and A42 have abend motif at residues V240K28, located near the loop region in the strand-loop-strand struc-ture of the bril, which has been suggested as a nucleation site for monomer folding (31, 32)(see Figure 5e). This bend is stabilized by a salt bridge between residues E22 and K28, whichis notable in light of familial Alzheimers mutations involving the E22 residue (33). Residues be-longing to the central hydrophobic core (L17A21, a highly aggregate-prone region that formsbrils if excised from the protein) and to the I31V36 region adopt a -strand structure in bothA40 and A42. These same regions are found in a -strand structure in the context of the bril.A42 further populates a hairpin in the C-terminal region (V39I41), also seen in simulations ofisolated fragments of the terminus (34). These simulations suggest that modeling the monomericstructure, and identifying regions of transient secondary structure, can provide important cluesabout the aggregation pathways and the role of point mutations in modulating aggregation. Themost important result from these simulations is the identication of possible aggregation-pronestructures among a diverse family of existing structures.

Similarly, in the case of the IAPP peptide, simulations on aggregating and nonaggregatingforms of the peptide have revealed signicant differences in monomeric structure, with aggre-gating variants (e.g., human IAPP) populating both compact and extended conformations, andnonaggregating variants (e.g., rat IAPP) exhibiting only compact structures (3537). Structuresgenerated from REMD or metadynamics simulations can serve as starting points for further sim-ulations of the interaction of inhibitor molecules (e.g., EGCG) with amyloidogenic peptides.



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Systematiccoarse graining

CG

ALAPHE

VALLYS

Simplemodels

bipi

si

Higher-resolutionmodels

N*a b

Phenomenologicalmodels

A40 A42

Atomisticmodels

PRIME

Binding ofPIB to fibrils

Monomer

OPEP

MARTINI MARTINIwater

XX

HH

EEEE

HH HH

XX XXXX

YY YY YY YY YY YY YYXX

PP PP A()A()C(+)C(+)

XX XX

cc d e

Figure 5Different resolution models for the study of protein aggregation, from coarse grained to atomistic. (a) Simple models: the orientablestick model (19) and the sphero-cylindrical model (20). (b) Phenomenological models: the lattice model (21), Caisch model (22), andShea model (23). (c) Systematic coarse graining: a coarse-grained polyalanine chain (24). (d ) High-resolution models: the MARTINImodel (15), PRIME model (17), and OPEP model (16). (e) Atomistic models of the Alzheimer amyloidpeptide: monomers fromreplica exchange molecular dynamics simulations, adapted from Reference 25, and PIB bound to brils, adapted from Reference 26.

It is important to note that different force elds can lead to somewhat different secondarystructure predictions, particularly in the case of intrinsically disordered peptides, such as Aand IAPP. Most force elds have been parameterized on the basis of folded motifs and may needreoptimization to better account for the unfolded/partially folded nature of intrinsically disorderedpeptides.

In addition to probing the early stages of aggregation, atomistic simulations have also beeninstrumental in studying the structural characteristics of brils. Starting with coordinates obtainedfrom solid-state NMR, investigators have proposed and rened models for amyloid brils of Aand IAPP (3841). These bril structures have been used to gain insight into the binding andmodeof action of amyloid dyes and small molecule inhibitors (42, 43). For instance, in simulations,thioavin T (ThT) and its derivative PIB would recognize and bind to the hydrophobic andaromatic grooves formed on the -sheet surface of A40 and A42 brils, and in the case ofA42, there is an additional binding mode in the loop region of the bril (see Figure 5e) (26).Further simulations with Congo Red revealed a new binding site, not seen for ThT and PIB, inwhich the molecule bound to the edge of the bril (44), as seen in simulations involving anti-inammatory drugs (45), possibly explaining the inhibitory role of Congo Red in blocking brilextension.

Atomistic simulations have also probed the growth phase of bril formation (see Figure 2).For instance, Bolhuis and coworkers (46) used transition path sampling (discussed in Section 4)to study the mechanism of bril elongation. Their simulations conrmed the proposed dock-lockmechanism (47), showing that the docked state was indeed an intermediate on the elongation



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pathway and that the lock process could proceed by more than one pathway (either by the ini-tial formation of hydrogen bonds, followed by side-chain reorientation, or vice versa). Anotherexample of the use of atomistic simulations to study elongation can be found in the work of Wangand coworkers (48), who used REMD simulations to show that brils with a cross- structurecould be a template for the formation of additional structure in A monomers.

3. COARSE-GRAINED MODELS

The coarse-graining technique is well suited to the study of peptide aggregation. First, the min-imum timescales and length scales required to capture the aggregation process are in generalsignicantly higher than those for protein folding (Figures 3 and 4). Second, although atomisticsimulations can capture the initial stages of aggregation (up to roughly tetramers) and model pre-formed small brils, the full assembly process from monomers to the bril is beyond the currentcomputational reach of all-atom simulations. Third, the structural similarity between amyloidbrils composed of different peptides seems to imply a degree of universality in the mechanism ofbril formation (6), lending support to the use of simplied peptide models that omit some molec-ular details yet retain the essential physical elements governing aggregation. Fourth, the techniqueworks well for studying the interaction between peptide aggregation and other biomolecules inthe cellular milieu, such as membranes (4954) and other lipid structures (22, 55, 56). Finally,these coarse-grained simulations are ideal to study systems that use a solid surface as a substrateon which aggregates adsorb, a setup common in many experiments (e.g., atomic force microscopy)(5764).

A wide spectrum of coarse graining is possible (65, 66). Some models are very lightly coarsegrained, keeping atomistic resolution for the backbone but coarse graining the side chain. At theother extreme, coarse graining can be done on the molecular scale and beyond.

3.1. Lower-Resolution Models

Coarse graining comes with the trade-off of accuracy and computational efciency, and the degreeof coarse graining should depend on the smallest important length scale of the system of study. Inpractice, however, it is nontrivial to determine a priori whether the small coarse-grained lengthscales affect the physics of aggregation. This difculty is especially acute in aggregation becauseof the extreme range of length scales and timescales involved (Figure 3).

Highly coarse-grained models sacrice sequence-level resolution. Representative models areshown in Figure 5a. For instance, Barz & Urbanc (67) studied the general properties of aggrega-tion using a minimalistic tetrahedral model with varying numbers of hydrophobic and hydrophilicbeads, whereas Auer et al. (68) developed a tube model, and Zhang & Muthukumar (69) devel-oped a simple cuboid model capable of capturing the essence of the nucleation growth mechanism.Wallin and colleagues (19) simulated more than 105 peptides, represented by sticks (with denedorientations about their axes) placed on a cubic lattice, using Monte Carlo simulations. They ob-served a nucleation growth mechanism in which the brils needed to form a sufcient number ofvertical layers before they could extend longitudinally. Low-resolution models have also been em-ployed in conjunction with a dynamic Monte Carlo method, designed to capture kinetics withinthe Monte Carlo framework by making the moves sufciently small that each one is physical.Vacha and colleagues (20) studied a generic two-state peptide: one representing a soluble randomcoil and the other a bril-prone -sheet conformation. They used an implicit water model andsimulated 600 peptides at concentrations ranging from 0.2 to 8.0 mM. Their system exhibitedbrillar self-assembly after the formation of a critical nucleus, which they determined to be a



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partially converted mixed aggregate. The aggregates conversion to a full -sheet structure was amultistep process.

Efforts in coarse graining extend beyond the molecular length scale. Buehler and colleagues(70) developed a very highly coarse-grained model that represents the bril itself as a chain ofcoarse-grained beads. Their mesoscale model is designed to study the self-assembly of thesestrands. Elastic parameters are obtained from implicit water all-atom simulations and used toparameterize the coarse-grained model. The authors looked at the plaque assembly of 240 brils,determining that, for sufcient length, adhesion forces between brils induce bending, which cangenerate entangled/disordered plaques, ring-like geometries, and self-folded brils. Conversely,shorter brils form ordered, rigid assemblies.

3.2. Phenomenological Models

A higher level of resolution than is achievable with the models presented in the previous sectioninvolves coarse graining over atomic length scales, with one or more beads representing an aminoacid. These simple physics-based models have been quite successful in elucidating which of aproteins physical properties play a key role in the aggregation process. Instead of representingthe full spectrum of amino acid residues, these models typically use generic amino acid types, suchas charged, polar, hydrophobic, or neutral.

One of the simplest phenomenological models is the lattice model, which restricts the allowedcoordinates to a cubic lattice and typically employs a low level of resolution (a single bead) (71), al-though it also allows for amultibead description of the amino acid (72). Simple latticemodels, suchas the work by Li and coworkers (21), were capable of identifying aggregate-prone conformations(the N conformation shown in Figure 5b).

Phenomenological models can also be off-lattice, of low to mid-resolution. Examples includetheCaischmodel (22, 73, 74) (two beads per residue) and the Sheamodel (23, 75) (three beads perresidue). These phenomenological models focus on how the peptide -sheet propensity affects thekinetics of bril formation fromdimers to longer brils of tens of peptides. As initial congurationsoften involve peptides scattered over a volume of thousands of cubed nanometers, they typicallyemploy implicit solvent models to avoid lling such a volume with explicit water.

The Caisch model (Figure 5b) represents the peptide as possessing one of two possiblecongurations, a folded conformation and a -competent conformation, with a dihedral potentialdesigned to bias both to different degrees.The-sheet propensity parameter in thismodel controlsthe depth of the potential energy well of the folded conformation (76). With this model, the mostamyloidogenic proteins exhibit features that are distinct from those of less amyloidogenic ones(73). Fibril formation occurs rapidly along a single pathway following a smaller nucleus, withoutthe formation of intermediates such as micelles or protobrils. The bril growth rate depends farmore strongly on concentration. Any polymorphism in the brils is determined by external con-ditions rather than being under kinetic control (77). Furthermore, brils are found to be cytotoxiconly during their growth phase. Fibril formation is accelerated by membranes and is not signif-icantly decelerated by surfactants or accelerated by macromolecular crowding (22, 78). Proteinsfalling into the highly amyloidogenic category include Phe-Phe, GNNQQNY, transthyretin,and A40. More weakly amyloidogenic proteins include A42, Sup35, prion proteins, andmyoglobin.

The Shea peptide model uses three beads per residue: two for the backbone and one for theside chain (Figure 5b). Similar to the Caisch model, the Shea model controls -sheet propensityvia a backbone dihedral potential. However, instead of modulating the relative well depths of -competent and -protected conformations, it controls the resistance to backbone torques against



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deviations from the preferred off-trans conguration of the side chains. Stiffer peptides are shownto be more prone (23). Both models were able to distinguish between different aggregationpathways, with peptides with high -sheet propensity forming brils via an ordered -sheetnucleus, whereas peptides of lower -sheet propensity rst formed disordered oligomers fromwhich the structure then emerged. In addition to their use in studying the nucleation step, thesemodels could also beused in seeding simulations to studybril growth.An important outcome fromthese simulations is the observation of both bril elongation (standard growth mechanisms) andlateral bril growth (secondary growth mechanism) (75, 7981). The Shea group (49) studied theaggregation of 32 short -sheet-prone peptides on the hydrophilic surface of a bilayer comprising648 lipids in an implicit solvent. This work combines a coarse-grained peptide amyloid model (23)with the Brannigan-Brown coarse-grained lipid bilayer model (82). They found that, similar to anattractive solid surface (83), the membrane was biased toward -sheet morphologies. However,unlike a solid surface, membrane undulations increased dynamic transitions between aggregatestructures and disrupted the formation of multiple bril layers parallel to the surface. Additionally,the authors observed several effects on the membrane: reduced uctuations, increased bendingmodulus, and a local ordering of lipid head groups to conform to optimal packing with the brilshydrophilic residues. These effects were locally constrained to the position of the brils and didnot seed a large-scale phase transition in the membrane.

3.3. MARTINI Force Field

More detailed representations of the protein are necessary to capture specic chemical properties.The MARTINI force eld is the most widely used coarse-grained atom model at this resolution,combining groups of (on average) four heavy atoms as a single bead (15, 51, 8489) (Figure 5d ).The MARTINI water model similarly maps four water molecules per bead. For bonded interac-tions, it matches to an all-atom reference, but nonbonded interactions are chosen based on thechemistry of the united atoms (i.e., their charge, polarity, and hydrogen bonding capabilities) (90).By selecting nonbonded potentials based on identiable chemical properties rather than system-specic optimization to all-atom simulations (systematic coarse graining), themodel is transferableto many different molecules, including water, lipids, proteins, and (a work in progress) nucleicacids. A known issue of the MARTINI model with respect to protein aggregation is its neglectin the detail of the peptide backbone (90). The Tieleman group (85) has recently improved theMARTINI potentials to better capture amyloid assembly.

Examples of the use of the MARTINI model to study bril formation include work bySchitt and colleagues (88), who explored the effects of longitudinal versus lateral growth. Theyemployed a coarse-grained MARTINI model to represent 27 protobril fragments of amylin(SNNFGAILSS), with each protobril consisting of 20 peptides (2029). The simulation fol-lowed the merging of these protobrils. They found that the growth mechanism was temperaturedependent, preferring elongation over lateral growth at lower temperatures, a preference lost asthe temperature increased. Schatz and colleagues (86) simulated the self-assembly of peptide am-phiphiles into bers, running a system of 400 peptides for 16 s using the MARTINI model inexplicit water. They found that the system rst formed spherical micelles, which arranged intoa three-dimensional network of micelles held by van der Waals interactions. The micelles thenmerged to form an extended ber. In a high-throughput study, Tuttle and colleagues (89) used theMARTINI model in explicit water to test the aggregation propensity of 400 different dipeptidecombinations. Each test consisted of 300 dipeptides run for 100 ns. Systems exhibiting a strongaggregation propensity were then selected for more extensive simulations. This method can beuseful to rapidly nd aggregation-prone sequences.



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Several recent computational studies have looked at the effect of membranes on protein aggre-gation using coarse-grained models. Using a MARTINI model with 16 proteins, 7,000 lipids, andcoarse-grained water, Sansom and colleagues (54) showed that the morphology of transmembraneprotein aggregates depended on several factors. Hydrophobic mismatch (i.e., the size of the pro-teins hydrophobic region relative to the thickness of the membranes hydrophobic core) can driveprotein aggregation. The protein class (helix versus barrel) and membrane curvature also affectthe aggregate morphology. Li & Gorfe (51) conducted a MARTINI model simulation with 32H-Ras proteins aggregating on a lipid bilayer (7,320 lipids). Coarse-grained simulations of pep-tide aggregation on small lipid micelles, comparable in size to the aggregates themselves, wereconducted by Hung & Yarovsky (56). These simulations used a MARTINI model with 125 lipidsand 27 apoC-II(6070) peptides, and 20,000 water beads. They showed a substantial reduction inthe aggregation rate for free lipids compared to bulk aggregation. The aggregate morphology wasstrongly dependent on the local lipid environment: Greater hydrophobic contact with the lipidsresulted in elongated aggregate structures. Additionally, the presence of peptides disrupted lipidassembly. Tieleman and colleagues (85) looked at the aggregation of 1, 8, and 64 octapeptides[SNNFGAIL and (GV)4] at an explicit water-octane interface using an extension of the MAR-TINI model. They found more extended morphologies at the interface than they observed in bulkwater. Adsorption was rapid, forming stretched conformers resembling strands.

3.4. The PRIME Model and Discontinuous Molecular Dynamics

A similar resolution model, PRIME (and the more recent PRIME20), has been employed exten-sively by Hall and colleagues (17, 9196) to study the kinetics of bril formation (Figure 5d ).They used discontinuous molecular dynamics (DMD), which allows for discontinuous breaks inthe energy functional by computing the reection/transmission of particles across the discontinu-ity. PRIME reduces the number of particles to four per amino acid and is able to effectively capturethe energetics of hydrogen bonding using an efcient directional square-well hydrogen bond. Theparameterization philosophy for PRIME is to reduce the number of interaction parameters, suchthat each parameter is physically meaningful, but to retain structural discrimination (17).

Hall and colleagues (91) studied the aggregation kinetics of 192 peptides (sequence KA14K)into a single bril, averaged over 30 independent simulations. Fibrils for this system formed bythe intermediate of amorphous aggregates that, given sufcient size, spontaneously ordered into sheets (i.e., the nucleation growth mechanism), which subsequently extended by the addition ofmonomers to the ends, one at a time (templated assembly). They also simulated the brillization of48 tau fragment peptides (sequence VQIVYK) at varying temperatures (92). They contrasted twohydrogen bond constraints: one favoring parallel sheets and one with no bias to parallel versusantiparallel. The parallel-biased constraints were more consistent with X-ray crystallography (97).At sufciently high temperatures, brils formed quickly by a templating mechanism.

Further simulations with the PRIME20 model were performed on seven different sequences,each system using 48 peptides (93). Their brillization propensity agreedwith experimental results(98, 99) at sufcient temperature. Hall et al. hypothesized that the brillization transition temper-ature in their model can predict a sequences bril propensity. In PRIME simulations, they studiedthe bril formation of palindromic sequences: Syrian hamster prion protein SHaPrP(113120)(AGAAAAGA),mouse prion protein MoPrP(111120) (VAGAAAAGAV), and eight variations onthese (94).Their analysis of howkinetic events inuencemorphology demonstratedhow sequenceswith long stretches of hydrophobic residues decrease brillar order in preference of a disordered,collapsed state. The Hall group (95) also employed the PRIME model to study the formation oftwisted A(1622) brils, implicated in Alzheimers disease. They found a temperature-dependent



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mechanism similar to their later tau fragment study (i.e., a nucleation growth mechanism at lowtemperature and templated assembly at high temperature) (92). They observed the formation ofstructural details (e.g., intersheet distance, antiparallel sheets, side-chain interdigitation) con-sistent with experiments (97, 100102).

The Hall group is not the only group to use DMD to study peptide aggregation. In a recentstudy, Auer and colleagues (103) contrasted the contributions of kinetics and thermodynamics inprotein aggregation. They represented the proteins by a chain of hard spheres centered on theC atoms, with sequence-dependent hydrogen bonding (104). They simulated 125 12-residuepeptides using DMD with an implicit solvent. They determined that kinetics were essential foraggregate formation and suggested that kinetics allow amyloidogenic proteins to fold into theirnative, aggregation-immune state, even when these simulations give the bril conformation asbeing more thermodynamically stable. Urbanc and colleagues (105107) conducted a number ofrecent studies on the oligomerization of A using coarse-grained DMD simulations, as well ashighly coarse-grained DMD simulations of generic properties of aggregation using a tetrahedralprotein model (67). Additionally, Dokholyan et al. employed DMD simulations to study the ag-gregation of A with a coarse-grained model with two beads per residue (108) and the aggregation(109) and dimerization (110) of SOD1 with a two-bead and atomistic model, respectively.

3.5. The OPEP Model

OPEP is a high-resolution coarse-grained model that has a high degree of chemical specicitywithout imposing articial constraints on the secondary structure (16) (Figure 5d ). Althoughit represents the side chain as a single coarse-grained bead, the backbone is given full atomicresolution for the heavy atoms.

Mousseau and colleagues (111) studied the dimerization of various alloforms of A usingOPEPwith a combined temperature and Hamiltonian replica exchange methodology. They showed thatthe dimerization propensity of the peptides is strongly affected by the Ile41 and Ala42 aminoacids and the salt bridge located at D23K28. Similarly, Derreumaux and colleagues looked at theequilibrium structures of A(2535) trimers and hexamers (112) and have conducted studies ofthe trimer structures of A(1742) (113) using the OPEP model with REMD. Additionally, theysaw how the latter structure is affected by ve different small molecule inhibitors. Their resultsshowed multiple binding modes of the drugs to the trimer and suggested that different drugs mayhave varying efcacy at different stages of oligomerization.

The OPEP force eld was also used to study the early stages of oligomerization of the NNQQand GNNQQNY peptides derived from the yeast prion Sup35 (114, 115). For the GNNQQNYpeptide, Mousseau and colleagues (115) employed REMD with system sizes up to 20-mers. Largerbrils were able to form transiently but destabilized into globular/disordered forms. The authorspredicted a high degree of polymorphismof the sequence.Using conventionalmolecular dynamicssimulations, they also analyzed the oligomerization kinetics of the same sequence (116). Theyfound kinetics mostly consistent with classical nucleation theory, with a critical nucleus of four tovemonomers.However, deviations from this theory occurred via rearrangements of the structurepostnucleation. They observed signicant polymorphism in the 20-mer.

4. DEVELOPMENTS IN COMPUTATIONAL METHODS

Table 1 presents a selection of computational techniques that have been (or could be) appliedto the study of protein aggregation. We discuss some of these techniques in more detail in thesubsequent sections.



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Table 1 Selection of computational techniques for the study of protein aggregation

Computationaltechnique Method Description Reference(s)Thermodynamicenhanced samplingmethods

Metadynamics Enhanced sampling of free energy landscape usingcollective variables; adaptive method; kinetics are lost

Method (117);applications(118121)

Umbrella sampling Enhanced sampling of free energy landscape usingcollective variables; kinetics are lost

Method (122);applications(123, 124)

Parallel tempering(temperature REMD)

Enhanced sampling of free energy landscape using runsat multiple temperatures; kinetics are lost


Replica exchangemolecular dynamics(REMD)

Enhanced sampling of free energy landscape usingmultiple temperatures (parallel tempering) and/orvarying Hamiltonian parameters; kinetics are lost

Method (125, 126);applications (83,111115, 127, 128)

Replica exchangestatistical temperaturemolecular dynamics

Replica minimization required for good sampling inREMD; adaptive method

Method andapplications(129, 130)

Replica exchange MonteCarlo

As for REMD, but for Monte Carlo sampling Method (131);applications (132)

Kinetic enhancedsampling methods

Markov state model Enhanced sampling of kinetics using collective variables;launches short trajectories from congurationsrequiring the greatest sampling; adaptive method

Method (133, 134);applications(135, 136)

Free energy guidedsampling

Enhanced sampling of kinetics using approximated freeenergy surface; launches short trajectories in parallelwith Boltzmann distribution; adaptive method

(137)

WExplore Enhanced sampling of kinetics using multiple replicas indynamically assigned tessellations of congurationspace; clones/merges replicas as needed; collectivevariable method; adaptive method

(160)

Transition pathsampling

Rare-event sampling method, well suited to studyprocesses, such as protein folding and aggregation, thathave complex underlying energy landscapes; involvesgenerating a set of reactive trajectories between aninitial and nal state, typically followed by likelihoodmaximization to obtain optimized reaction coordinates

(138140)

String method Free energy landscape method to nd lowest barrierpath (mountain pass) between two states; parallelruns are tied together in a string in state space toprevent them from merging/separating; the stringconverges to the transition path between the ends

(141, 142)

Data/trajectoryanalysis methods

Secondary nucleationkinetic analysis

Analysis of trajectory/experimental brillization kineticdata; involves tting to a master equation, includingsecondary pathway terms

(2, 8, 9, 143)

Normal mode analysis Trajectory analysis method using elastic networkmodels; used to study the low-frequency collectivemotions of biomolecules

Method (144, 145);applications(146, 147)

(Continued )



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Table 1 (Continued)

Computationaltechnique Method Description Reference(s)Systematic coarsegraining

Relative entropy coarsegraining

Systematic coarse-graining method matchingcoarse-graining to all-atom congurational probabilitydistributions for minimal information loss

Method (148);applications (24)

Multiscale coarsegraining

Systematic coarse-graining method matchingcoarse-graining to all-atom momenta


Iterative Boltzmanninversion

Systematic coarse-graining method matchingcoarse-graining to all-atom Boltzmann distributions

Method (151);applications (152)

Fast moleculardynamicsintegrator

Discontinuous moleculardynamics

Molecular dynamics integrator allowing fordiscontinuous potentials

Method (153);applications(17, 9195, 103)

4.1. Systematic Coarse Graining

Systematic coarse graining provides a bottom-up methodology to obtain the optimum coarse-grained potentials matching the behavior of all-atom simulations or experimental data. Recentdevelopments of this technique include the relative entropy method by Shell (148), the multiscalecoarse-graining method by Izvekov & Voth (149), and the iterative Boltzmann inversion methodby Muller-Plathe and colleagues (151). The relative entropy method uses information theory tond the potentials with minimal information loss in the congurational ensembles (148). The rel-ative entropy is dened as the sum over the conguration space of Srel = PT ln(PT/PM), where PTis the probability of this conguration in the target (all-atom) ensemble, and PM is its probabilityin the model (coarse-grained) ensemble. The relative entropy method minimizes Srel. Multiscalecoarse graining is a variational technique that best matches all-atom momenta in the coarse-grained sites (149). The goal of this method is to minimize (in force eld parameter space) thesquare of the difference between the momenta of the reference force eld and coarse-grained forceeld (154). The method accomplishes this by breaking the coarse-grained force eld into long-range (Coulomb) and short-range (to be optimized) components. The short-ranged componentis approximated as a polynomial spline, which allows for an efcient least-squares optimization byexpressing it as an overdetermined system of linear equations. The iterative Boltzmann inversionmethod is designed to reproduce all-atom Boltzmann statistics (151). The procedure begins withan initial guess of the potential and a set of collective variables used to compare the referenceand coarse-grained force elds. For each probability distribution function p(n), where ndenes the conguration of the system (e.g., bond lengths, dihedral angles), the estimated freeenergy of the coarse-grained system at the i-th iteration [kBT ln(pi (n))] will differ from the freeenergy of the reference. The updated potentials become Vi+1(n) = Vi (n)kBT ln(pi (n)/p(n)).This iterative procedure converges to a potential at which pi (n) p(n).

One primary drawback to systematic coarse-grained methods is that they already necessitateobtaining good all-atom statistics to parameterize the coarse-grained model (155). Additionally,these potentials are system specic and in principle would require reparameterization of all inter-actions if the system changed in any way. These methods are ideal for studying the self-assembly ofmany identical molecules, as the inter- and intramolecular potentials are typically obtained froma system of fewer molecules (assuming that the optimal potentials do not include direct many-body interactions between several molecules).Many systematic coarse-grainedmethods have beenapplied to aggregation (24, 55, 150, 152).



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Carmichael&Shell (24) applied the relative entropymethod to the self-assembly of polyalanine,(Ala)15. At least three beads per alanine were needed to capture the -helical and -hairpinstructures of the folded peptide. Simulating 25 copies of (Ala)15, they found that the brillar orderemerged following the internal reorganization of a disordered intermediate.

The Voth group (150) applied the technique of multiscale coarse graining to a number ofprotein aggregation systems. They studied the aggregation of 27 polyglutamine peptides and sawan increase in the aggregation propensity with concentration and chain length. Additionally, theystudied how N-BAR proteins induce curvature changes in lipid vesicles (55). They simulatedvesicles 200300 nm in diameter with protein coverages ranging from 10% to 95%, immersedin explicit solvent. They then mapped the coarse-grained lipid coordinates onto a mesoscopiccontinuum model, with a eld variable describing the membranes protein composition. Thisallowed the simulations to be extended to timescales comparable with experiment. The topologyof the spherical vesicle was dramatically altered into a tubular network. This change was associatedwith the linear ordering of protein aggregates, which is believed to drive the formation of reticularmembrane structures in vivo.

Peter and colleagues (152) studied the aggregation of oligoalanine peptides, employing anothersystematic coarse-graining method based on iterative Boltzmann inversion. They found that cer-tain microscopic details lost in the coarse-graining process can be recovered by backmapping toatomistic coordinates.

4.2. Thermodynamic Methods

Both atomistic and coarse-grained simulations combine well with enhanced sampling methodsto increase the sampling of Boltzmann-disfavored morphologies in order to compute free energyproles more efciently. Some of these bias sampling on prespecied collective variables, suchas metadynamics (117) or umbrella sampling (122). Parallel tempering (or temperature replicaexchange) does not require the specication of collective variables; instead, it increases samplingby exchanging trapped systems with a higher temperature (125).

Replica exchange enhances sampling by launching parallel simulations that each explore aspecic point in the parameter space. If this parameter is temperature, then the method is alsoknown as parallel tempering. In this method, parallel trajectories are launched, each with its ownparameter value (we discuss temperature for simplicity) (Figure 6). At regular intervals, eachtrajectory is given an opportunity to swap with trajectories at neighboring temperatures accordingto a Metropolis criterion that enforces the correct thermodynamics. The probability of swappingreplicas i and j is determined by the value of = (i j )(U j U i ), where i = 1/kBTi , and Uiis the potential energy of the current state of replica i. If 0, the swap always occurs; otherwise,the swap probability is Pswap = exp(). The swapping procedure necessitates each parameterhaving discontinuous trajectories, so correct kinetics are lost. Replica exchange can be employedwith both Monte Carlo and molecular dynamics simulations (125, 131). The replica exchangemethodology has been used in the atomistic simulations described earlier in this review, as well asin a number of coarse-grained simulations (72, 83, 111115, 127, 128).

The replica exchange statistical temperature molecular dynamics algorithm, developed byKeyes and colleagues (129), is an improvement on the usual temperature replica exchange al-gorithm designed to minimize the number of replicas required for good sampling. The issue iscaused by the necessity of substantial energy overlap in neighboring replicas to maintain a hightemperature swap rate. It relies on the statistical temperature molecular dynamics algorithm (130)to give a more even energy sampling and a self-adjusting weight. This method has been appliedto protein folding (129) but to our knowledge has not yet been applied to aggregation.



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a Metadynamics

T1

T2

TN

b Replica exchange

Figure 6Two commonly used simulation methods for the study of protein aggregation. (a) Metadynamics. Regions ofstate space frequently visited ll up with Gaussian hills, biasing away from well-sampled states. (b) Replicaexchange molecular dynamics simulations. Parallel replicas swap to overcome free energy barriers.

Umbrella sampling is a technique in which a dened collective variable is held by a potentialwell at a particular target value.Multiple trajectories are launched at varying target values such thatthe statistics of neighboring umbrellas overlap. Umbrella sampling forces the system into regionsof state space that would otherwise have poor sampling. Because the bias potential is known, thestatistics of the unbiased potential can be recovered from the biased statistics. This is a usefultechnique for determining the energy of the separation of monomers, as this separation can bereadily dened as a collective variable, as done by the Thirumalai group (123). Similarly, Davis &Berkowitz (124) used this technique to bind A to a lipid bilayer and determined that the bindingpromoted conversion to aggregate-prone conformations.

Metadynamics is another technique involving enhanced sampling over collective variables usinga biased potential to force the system to sample low-probability states (117). However, unlikeumbrella sampling, metadynamics is an adaptive method, automatically biasing congurationsaway from those most visited to make the sampling more efcient. Similar to umbrella sampling,the bias is accounted for to deduce the correct unbiased statistics of the system. More specically,the method periodically adds a small Gaussian hill to the potential energy of the current region ofstate space. Thus, regions that are frequently sampled are given a negative bias, eventually forcingthe system into rarer congurations. In the limit of t , the total potential energy will become



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at as all the wells ll up with accumulatedGaussian hills. Onemust choose the extra parameters ofthis method (hill height, width, and frequency) with care to ensure that the statistics do not dependon them. This technique has been used to study congurations of amyloidogenic proteins (119121, 156). A schematic comparison of replica exchange and metadynamics is given in Figure 6.

4.3. Kinetic Methods

The aforementioned methods lose kinetic information, by either biasing the sampling of collectivevariables or giving discontinuous trajectories at constant temperature. Other sampling methodspreserve kinetics by launching many short, parallel trajectories, and it is the judicious choice ofhow to launch these trajectories that enhances sampling.

The Markov state model (MSM) formalism has lately been applied to the study of biomolecularsimulation (133, 157, 158). This approach increases sampling by launching parallel trajectories.The basic idea behind MSM is to bin sets of congurations in state space and model the systemas a set of Markovian transitions between these congurations, thereby generating a kinetic mapof transition probabilities between states. This method is well suited to sampling the kineticlandscape because it adaptively selects starting congurations that require additional sampling.It is important to follow up the MSM simulations with a verication that the transitions areMarkovian (history independent) to ensure self-consistency. It is also necessary to use a good statespace decomposition of the collective variables (collective variable binning) (159). MSM providesa complementary approach to free energy methods such as replica exchange or metadynamics,which lose kinetics in favor of sampling the energy landscape.

A related method is free energy guided sampling, developed by Zhou & Caisch (137). It dif-fers from traditional MSM in that it uses an approximate free energy surface in place of collectivevariables to bias the starting congurations. This method iteratively launches short trajectories inparallel. It has two stages: exploration and renement. In the exploration stage, the initial trajecto-ries are launched and the conguration space binned. An MSM model is constructed based on theinitial simulations, and a rough free energy prole around the starting conguration is generated.This cycle is then restarted from free energy barriers farthest from the initial conguration. Therenement stage is designed to rene the calculated free energy surface. Trajectories are launchedfrom equally spaced initial congurations along the free energy surface, stopping when the calcu-lated free energy has converged. The authors have applied this method to protein folding, but toour knowledge, it has not yet been applied to aggregation.

The WExplore method developed by Dickson & Brooks (160) also biases the launching oftrajectories toward poorly sampled regions of conguration space, although unlike the MSMmethods it does not make the Markovian assumption for state transitions. It accomplishes thisusing a weight for each trajectory with which it contributes to statistical averages. Samplingregions are dened dynamically in conguration space, and trajectories are cloned and merged toencourage even sampling across these regions. The sampling regions are dened using a distancemetric (e.g., RMSD) in a possibly high-dimensional space of order parameters and take the form ofVoronoi polyhedra. Unlike the original weighted ensemble algorithm (161), the sampling regionscan be dened in a hierarchical fashion, which allows for the balancing of computational effortacross multiple length scales. Boltzmann sampling is achieved by changing the weight of eachtrajectory upon cloning steps (in which weights are split) and merging steps (in which weights areadded). Thus, replicas are forced to expand across the conguration space much faster than thefree energy surface would normally allow. This method has been applied to RNA conformationaldynamics (162) but would be well suited to protein aggregation as well.



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The kinetics of bril formation can also be inferred through secondary nucleation data analysismethods, such as those employed by Knowles and colleagues (2, 8, 9, 143). In this approach, onerepresents the kinetics as a function of an order parameter dening the degree of brillization. Thedata are t to a master equation that breaks down bril growth into several subprocesses. Theseinclude elongation, fragmentation, nucleation, and, recently (9), end-to-end association. The au-thors found that the lag phase cannot simply be described by the nucleation time of only theprimary pathway, highlighting the signicance of secondary nucleation. These analytical methodscan be used on both experimental data and simulation trajectories.

The normal mode analysis method (144, 145) is applied to an existing (typically all-atom)trajectory. It breaks the protein into coarse-grained sites and deduces collective motions of thebiomolecule from the vibrational network of pairs of these sites. Eom and colleagues (146) em-ployed this analysis on all-atom simulations to study elastic modes of an hIAPP bril (bending,torsion, stretching) for various structural hierarchies (e.g., parallel/antiparallel sheets and brillength). They showed how the bril structure affects its mechanical rigidity. The Buehler group(147) studied the elastic properties of A brils using normal mode analysis. They found thebrils Youngs modulus to be consistent with experimental values.

5. CONCLUSIONS

Above we review models of different resolutions, as well as a selection of simulation methodologiescommonly used to study protein aggregation. We focus on the aggregation process itself, withsome mentions of aggregation on surfaces and membranes. In principle, all the methods andmodels introduced here can be applied to the study of aggregation in a more cellular context. Thechallenge lies in the increased complexity of the system: To even begin to describe the cellularenvironment, one needs to take into account its many constituents (e.g., membranes, nucleic acids,osmolytes). This effort has already begun in earnest, and we anticipate signicant advances in thecoming years in our understanding of how the cellular environment modulates the aggregationprocess. Computational modeling shall continue to play a pivotal role in helping us understandthe nature of protein aggregation, providing an important complement to experimental studies.The near-boundless complexity arising from the extreme many-body nature of the problem willfuel the development of many more computational methods to come, ensuring the continuedsignicance of biomolecular simulation to the eld of protein aggregation.

DISCLOSURE STATEMENT

The authors are not aware of any afliations, memberships, funding, or nancial holdings thatmight be perceived as affecting the objectivity of this review.

ACKNOWLEDGMENTS

We acknowledge the support of a National Science Foundation (NSF) grant (MCB-1158577) andthe David and Lucile Packard Foundation. Additionally, we received support from the Center forScienticComputing from theCNSI,MRL, anNSFMaterials Research Science and EngineeringCenter (MRSEC) (DMR-1121053), and NSF CNS-0960316. This work was supported in partby the MRSEC Program of the NSF under award DMR-1121053. This work used the ExtremeScience and Engineering Discovery Environment (XSEDE), which is supported by NSF grants



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ACI-1053575 andTG-MCA05S027.We thankAndrij Baumketner, Scott Shell, ScottCarmichael,Zach Levine, and Catie Carpenter for assistance with the gures.

LITERATURE CITED

1. Chiti F,DobsonC. 2006. Proteinmisfolding, functional amyloid, and human disease.Annu. Rev. Biochem.75:33366

2. Knowles TP, Vendruscolo M, Dobson CM. 2014. The amyloid state and its association with proteinmisfolding diseases. Nat. Rev. Mol. Cell Biol. 15:38496

3. Knowles TPJ, Buehler MJ. 2011. Nanomechanics of functional and pathological amyloid material. Nat.Nanotechnol. 6:46979

4. Fitzpatrick AWP, Debelouchina GT, Bayro MJ, Clare DK, Caporini MA, et al. 2013. Atomic structureand hierarchical assembly of a cross- amyloid bril. Proc. Natl. Acad. Sci. USA 110:546873

5. Sunde M, Serpell LC, Bartlam M, Fraser PE, Pepys MB, Blake CC. 1997. Common core structure ofamyloid brils by synchrotron X-ray diffraction. J. Mol. Biol. 273:72939

6. Thirumalai D, Klimov D, Dima R. 2003. Emerging ideas on the molecular basis of protein and peptideaggregation. Curr. Opin. Struct. Biol. 13:14659

7. Straub J, Thirumalai D. 2011. Toward amolecular theory of early and late events inmonomer to amyloidbril formation. Annu. Rev. Phys. Chem. 62:43763

8. Knowles TP, Waudby CA, Devlin GL, Cohen SI, Aguzzi A, et al. 2009. An analytical solution to thekinetics of breakable lament assembly. Science 326:153337

9. Michaels TC, Knowles TP. 2014. Role of lament annealing in the kinetics and thermodynamics ofnucleated polymerization. J. Chem. Phys. 140:214904

10. Friesner RA, Guallar V. 2005. Ab initio quantum chemical and mixed quantum mechanics/molecularmechanics (QM/MM) methods for studying enzymatic catalysis. Annu. Rev. Phys. Chem. 56:389427

11. Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M. 1983. CHARMM: aprogram for macromolecular energy, minimization, and dynamics calculations. J. Comput. Chem. 4:187217

12. Pearlman DA, Case DA, Caldwell JW, Ross WS, Cheatham TE III, et al. 1995. AMBER, a package ofcomputer programs for applying molecular mechanics, normal mode analysis, molecular dynamics andfree energy calculations to simulate the structural and energetic properties of molecules. Comput. Phys.Commun. 91:141

13. Christen M, Hunenberger PH, Bakowies D, Baron R, Burgi R, et al. 2005. The GROMOS software forbiomolecular simulation: GROMOS05. J. Comput. Chem. 26:171951

14. Jorgensen WL, Tirado-Rives J. 1988. The OPLS [optimized potentials for liquid simulations] potentialfunctions for proteins, energy minimizations for crystals of cyclic peptides and crambin. J. Am. Chem.Soc. 110:165766

15. Monticelli L, Kandasamy SK, Periole X, Larson RG, Tieleman DP, Marrink SJ. 2008. The MARTINIcoarse-grained force eld: extension to proteins. J. Chem. Theory Comput. 4:81934

16. Sterpone F, Melchionna S, Tuffery P, Pasquali S, Mousseau N, et al. 2014. The OPEP protein model:from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems. Chem.Soc. Rev. 43:487193

17. Cheon M, Chang I, Hall C. 2010. Extending the prime model for protein aggregation to all 20 aminoacids. Proteins 78:295060

18. Kinjo AR, Takada S. 2003. Competition between protein folding and aggregation with molecular chap-erones in crowded solutions: insight from mesoscopic simulations. Biophys. J. 85:352131

19. Irback A, Jonsson S, Linnemann N, Linse B, Wallin S. 2013. Aggregate geometry in amyloid brilnucleation. Phys. Rev. Lett. 110:058101

20. Bieler NS, Knowles TP, Frenkel D, Vacha R. 2012. Connecting macroscopic observables and mi-croscopic assembly events in amyloid formation using coarse grained simulations. PLoS Comput. Biol.8:e1002692



Ann

u. R

ev. P

hys.

Chem

. 201

5.66

. Dow

nloa

ded

from

ww

w.an

nual

revi

ews.o

rg A

cces

s pro

vide

d by

Uni

vers

ity o

f Wes

tern

Ont

ario

on

02/0

5/15

. For

per

sona

l use

onl

y.


21. Li M, Klimov D, Straub J, Thirumalai D. 2008. Probing the mechanisms of bril formation using latticemodels. J. Chem. Phys. 129:175101

22. FriedmanR,CaischA. 2011. Surfactant effects on amyloid aggregation kinetics. J.Mol. Biol. 414:3031223. Bellesia G, Shea JE. 2007. Self-assembly of -sheet forming peptides into chiral brillar aggregates.

J. Chem. Phys. 126:24510424. Carmichael SP, Shell MS. 2012. A new multiscale algorithm and its application to coarse-grained peptide

models for self-assembly. J. Phys. Chem. B 116:83839325. Rosenman DJ, Connors CR, Chen W, Wang C, Garcia AE. 2013. Amonomers transiently sample

oligomer and bril-like congurations: ensemble characterization using a combined MD/NMR ap-proach. J. Mol. Biol. 425:333859

26. Wu C, Bowers MT, Shea JE. 2011. On the origin of the stronger binding of PIB over thioavin T toprotobrils of the Alzheimer amyloidpeptide: a molecular dynamics study. Biophys. J. 100:131624

27. Best RB,Mittal J. 2011. Free-energy landscape of theGB1 hairpin in all-atom explicit solvent simulationswith different force elds: similarities and differences. Proteins 79:131828

28. Bitan G, Kirkitadze M, Lomakin A, Vollers S, Benedek G, Teplow D. 2003. Amyloid -protein (A)assembly: A40 and A42 oligomerize through distinct pathways. Proc. Natl. Acad. Sci. USA 100:33035

29. Bernstein SL, Dupuis NF, Lazo ND, Wyttenbach T, Condron MM, et al. 2009. Amyloid- proteinoligomerization and the importance of tetramers and dodecamers in the aetiology of Alzheimers disease.Nat. Chem. 1:32631

30. Ball KA, Phillips AH, Wemmer DE, Head-Gordon T. 2013. Differences in -strand populations ofmonomeric A40 and A42. Biophys. J. 104:271424

31. Lazo N, Grant M, Condron M, Rigby A, Teplow D. 2005. On the nucleation of amyloid -proteinmonomer folding. Protein Sci. 14:158196

32. Murray MM, Krone MG, Bernstein SL, Baumketner A, Condron MM, et al. 2009. Amyloid -protein:experiment and theory on the 2130 fragment. J. Phys. Chem. B 113:604146

33. Krone MG, Baumketner A, Bernstein SL, Wyttenbach T, Lazo ND, et al. 2008. Effects of familialAlzheimers disease mutations on the folding nucleation of the amyloid-protein. J. Mol. Biol. 381:22128

34. WuC,MurrayMM,Bernstein SL,CondronMM,BitanG, et al. 2009.The structure of A42C-terminalfragments probed by a combined experimental and theoretical study. J. Mol. Biol. 387:492501

35. Wu C, Shea JE. 2013. Structural similarities and differences between amyloidogenic and non-amyloidogenic islet amyloid polypeptide (IAPP) sequences and implications for the dual physiologicaland pathological activities of these peptides. PLoS Comput. Biol. 9:e1003211

36. Reddy AS, Wang L, Singh S, Ling YL, Buchanan L, et al. 2010. Stable and metastable states of humanamylin in solution. Biophys. J. 99:220816

37. DupuisNF,WuC, Shea JE, BowersM. 2009.Human islet amyloid polypeptidemonomers form ordered-hairpins: a possible direct amyloidogenic precursor. J. Am. Chem. Soc. 191:1828392

38. Miller Y, Ma B, Nussinov R. 2010. Polymorphism in Alzheimer A amyloid organization reects con-formational selection in a rugged energy landscape. Chem. Rev. 110:482038

39. Zhao J, Yu X, Liang G, Zheng J. 2011. Heterogeneous triangular structures of human islet amyloidpolypeptide (amylin) with internal hydrophobic cavity and external wrapping morphology reveal thepolymorphic nature of amyloid brils. Biomacromolecules 12:178194

40. Wu C, Bowers M, Shea JE. 2010. Molecular structures of quiescently grown and brain-derived poly-morphic brils of the Alzheimer amyloid A940 peptide: a comparison to agitated brils. PLoS Comput.Biol. 6:e1000693

41. Buchete N, Hummer G. 2007. Structure and dynamics of parallel-sheets, hydrophobic core, and loopsin Alzheimers Abrils. Biophys. J. 92:303239

42. Lemkul JA, Bevan DR. 2012. The role of molecular simulations in the development of inhibitors ofamyloid -peptide aggregation for the treatment of Alzheimers disease. ACS Chem. Neurosci. 3:84556

43. Ngo ST, Li MS. 2012. Curcumin binds to A140 peptides and brils stronger than ibuprofen andnaproxen. J. Phys. Chem. B 116:1016575

44. Wu C, Scott J, Shea JE. 2012. Binding of Congo Red to amyloid protobrils of the Alzheimer A940peptide probed by molecular dynamics simulations. Biophys. J. 103:55057



Ann

u. R

ev. P

hys.

Chem

. 201

5.66

. Dow

nloa

ded

from

ww

w.an

nual

revi

ews.o

rg A

cces

s pro

vide

d by

Uni

vers

ity o

f Wes

tern

Ont

ario

on

02/0

5/15

. For

per

sona

l use

onl

y.


45. Takeda T, Chang WE, Raman EP, Klimov DK. 2010. Binding of nonsteroidal anti-inammatory drugsto Abril. Proteins 78:284960

46. Schor M, Vreede J, Bolhuis PG. 2012. Elucidating the locking mechanism of peptides onto growingamyloid brils through transition path sampling. Biophys. J. 103:1296304

47. Esler W, Stimson E, Jennings J, Vinters H, Ghilardi J, et al. 2000. Alzheimers disease amyloid propa-gation by a template-dependent dock-lock mechanism. Biochemistry 39:628895

48. Xi W, Li W, Wang W. 2012. Template induced conformational change of amyloid-monomer. J. Phys.Chem. B 116:7398405

49. Morriss-Andrews A, Brown FLH, Shea JE. 2014. A coarse-grained model for peptide aggregation on amembrane surface. J. Phys. Chem. B 118:842032

50. SimunovicM, Srivastava A, VothGA. 2013. Linear aggregation of proteins on themembrane as a preludeto membrane remodeling. Proc. Natl. Acad. Sci. USA 110:20396401

51. Li H, Gorfe AA. 2013. Aggregation of lipid-anchored full-length H-Ras in lipid bilayers: simulationswith the MARTINI force eld. PLoS ONE 8:e71018

52. Pannuzzo M, Milardi D, Raudino A, Karttunen M, La Rosa C. 2013. Analytical model and multiscalesimulations of Apeptide aggregation in lipid membranes: towards a unifying description of conforma-tional transitions, oligomerization and membrane damage. Phys. Chem. Chem. Phys. 15:894051

53. SantoKP, BerkowitzML. 2012.Difference betweenmagainin-2 andmelittin assemblies in phosphatidyl-choline bilayers: results from coarse-grained simulations. J. Phys. Chem. B 116:302130

54. Parton DL, Klingelhoefer JW, Sansom MS. 2011. Aggregation of model membrane proteins, modulatedby hydrophobic mismatch, membrane curvature, and protein class. Biophys. J. 101:69199

55. Simunovic M, Mim C, Marlovits TC, Resch G, Unger VM, Voth GA. 2013. Protein-mediated trans-formation of lipid vesicles into tubular networks. Biophys. J. 105:71119

56. Hung A, Yarovsky I. 2011. Inhibition of peptide aggregation by lipids: insights from coarse-grainedmolecular simulations. J. Mol. Graph. Model. 29:597607

57. Keller A, Fritzsche M, Yu YP, Liu Q, Li YM, et al. 2011. Inuence of hydrophobicity on the surface-catalyzed assembly of the islet amyloid polypeptide. ACS Nano 5:277078

58. ZhuM, Souillac P, Ionescu-Zanetti C,Carter S, FinkA. 2002. Surface-catalyzed amyloid bril formation.J. Biol. Chem. 277:5091422

59. Kowalewski T, Holtzman DM. 1999. In situ atomic force microscopy study of Alzheimers -amyloidpeptide on different substrates: new insights into mechanism of -sheet formation. Proc. Natl. Acad. Sci.USA 96:368893

60. Green JD, Goldsbury C, Kistler J, Cooper GJS, Aebi U. 2004. Human amylin oligomer growth andbril elongation dene two distinct phases in amyloid formation. J. Biol. Chem. 279:1220612

61. Losic D, Martin LL, Aguilar MI, Small DH. 2006.-amyloid bril formation is promoted by step edgesof highly oriented pyrolytic graphite. Peptide Sci. 84:51926

62. Giacomelli CE, Norde W. 2003. Inuence of hydrophobic Teon particles on the structure of amyloid-peptide. Biomacromolecules 4:171926

63. HaC, ParkCB. 2006. Ex situ atomic forcemicroscopy analysis of-amyloid self-assembly and depositionon a synthetic template. Langmuir 22:697785

64. OBrien EP, Ziv G, Haran G, Brooks BR, Thirumalai D. 2008. Effects of denaturants and osmolytes onproteins are accurately predicted by the molecular transfer model. Proc. Natl. Acad. Sci. USA 105:134038

65. WuC, Shea JE. 2011. Coarse-grained models for protein aggregation.Curr. Opin. Struct. Biol. 21:2092066. Morriss-Andrews A, Shea JE. 2014. Simulations of protein aggregation: insights from atomistic and

coarse-grained models. J. Phys. Chem. Lett. 5:189990867. Barz B, Urbanc B. 2014. Minimal model of self-assembly: emergence of diversity and complexity.

J. Phys. Chem. B 118:37617068. Auer S, Meersman F, Dobson C, Vendruscolo M. 2008. A generic mechanism of emergence of amyloid

protolaments from disordered oligomeric aggregates. PLoS Comput. Biol. 4:e100022269. Zhang J, Muthukumar M. 2009. Simulations of nucleation and elongation of amyloid brils. J. Chem.

Phys. 130:03510270. Paparcone R, Cranford SW, Buehler MJ. 2011. Self-folding and aggregation of amyloid nanobrils.

Nanoscale 3:174855



Ann

u. R

ev. P

hys.

Chem

. 201

5.66

. Dow

nloa

ded

from

ww

w.an

nual

revi

ews.o

rg A

cces

s pro

vide

d by

Uni

vers

ity o

f Wes

tern

Ont

ario

on

02/0

5/15

. For

per

sona

l use

onl

y.


71. Li M, Co N, Reddy G, Hu C, Straub J, Thirumalai D. 2010. Factors governing brillogenesis ofpolypeptide chains revealed by lattice models. Phys. Rev. Lett. 105:218101

72. Ni R, Abeln S, Schor M, Stuart MAC, Bolhuis PG. 2013. Interplay between folding and assembly ofbril-forming polypeptides. Phys. Rev. Lett. 111:058101

73. Magno A, Pellarin R, Caisch A. 2012. Mechanisms and kinetics of amyloid aggregation investigated bya phenomenological coarse-grained model. InComputationalModeling of Biological Systems: FromMoleculesto Pathways, ed. NV Dokholyan, pp. 191214. New York: Wiley

74. Pellarin R, Caisch A. 2006. Interpreting the aggregation kinetics of amyloid peptides. J. Mol. Biol.360:88292

75. Morriss-Andrews A, Bellesia G, Shea JE. 2012. -sheet propensity controls the kinetic pathways andmorphologies of seeded peptide aggregation. J. Chem. Phys. 137:145104

76. Pellarin R, Guarnera E, Caisch A. 2007. Pathways and intermediates of amyloid bril formation.J. Mol. Biol. 374:91724

77. Pellarin R, Schuetz P, Guarnera E, Caisch A. 2010. Amyloid bril polymorphism is under kineticcontrol. J. Am. Chem. Soc. 132:1496070

78. Friedman R, Pellarin R, Caisch A. 2009. Amyloid aggregation on lipid bilayers and its impact onmembrane permeability. J. Mol. Biol. 387:40715

79. BellesiaG, Shea JE. 2009. Effect of-sheet propensity on peptide aggregation. J. Chem. Phys. 130:14510380. Bellesia G, Shea JE. 2009. Diversity of kinetic pathways in amyloid bril formation. J. Chem. Phys.

131:11110281. Morriss-Andrews A, Shea JE. 2012. Kinetic pathways to peptide aggregation on surfaces: the effects of

-sheet propensity and surface attraction. J. Chem. Phys. 136:06510382. Brannigan G, Philips P, Brown F. 2005. Flexible lipid bilayers in implicit solvent. Phys. Rev. E 72:01191583. Morriss-Andrews A, Bellesia G, Shea JE. 2011. Effects of surface interactions on peptide aggregate

morphology. J. Chem. Phys. 135:08510284. ThotaN, LuoZ,Hu Z, Jiang J. 2013. Self-assembly of amphiphilic peptide (AF)6H5K15: coarse-grained

molecular dynamics simulation. J. Phys. Chem. B 117:96909885. Seo M, Rauscher S, Pome`s R, Tieleman DP. 2012. Improving internal peptide dynamics in the coarse-

grained MARTINI model: toward large-scale simulations of amyloid- and elastin-like peptides. J. Chem.Theory Comput. 8:177485

86. Lee OS, Cho V, Schatz GC. 2012. Modeling the self-assembly of peptide amphiphiles into bers usingcoarse-grained molecular dynamics. Nano Lett. 12:490713

87. Guo C, Luo Y, Zhou R, Wei G. 2012. Probing the self-assembly mechanism of diphenylalanine-basedpeptide nanovesicles and nanotubes. ACS Nano 6:390718

88. Srensen J, Periole X, Skeby KK, Marrink SJ, Schitt B. 2011. Protobrillar assembly toward theformation of amyloid brils. J. Phys. Chem. Lett. 2:238590

89. Frederix PW, Ulijn RV, Hunt NT, Tuttle T. 2011. Virtual screening for dipeptide aggregation: towardpredictive tools for peptide self-assembly. J. Phys. Chem. Lett. 2:238084

90. Marrink SJ, Tieleman DP. 2013. Perspective on the Martini model. Chem. Soc. Rev. 42:68012291. Phelps EM, Hall CK. 2012. Structural transitions and oligomerization along polyalanine bril formation

pathways from computer simulations. Proteins 80:15829792. Cheon M, Chang I, Hall CK. 2012. Inuence of temperature on formation of perfect tau fragment brils

using PRIME20/DMD simulations. Protein Sci. 21:15142793. Wagoner VA, Cheon M, Chang I, Hall CK. 2012. Fibrillization propensity for short designed hexapep-

tides predicted by computer simulation. J. Mol. Biol. 416:59860994. WagonerVA,CheonM,Chang I,Hall CK. 2011. Computer simulation study of amyloid bril formation

by palindromic sequences in prion peptides. Proteins 79:21324595. Cheon M, Chang I, Hall CK. 2011. Spontaneous formation of twisted A1622 brils in large-scale

molecular-dynamics simulations. Biophys. J. 101:249350196. Wagoner VA, Cheon M, Chang I, Hall CK. 2014. Impact of sequence on the molecular assembly of

short amyloid peptides. Proteins 82:14698397. Sawaya MR, Sambashivan S, Nelson R, Ivanova MI, Sievers SA, et al. 2007. Atomic structures of amyloid

cross- spines reveal varied steric zippers. Nature 447:45357



Ann

u. R

ev. P

hys.

Chem

. 201

5.66

. Dow

nloa

ded

from

ww

w.an

nual

revi

ews.o

rg A

cces

s pro

vide

d by

Uni

vers

ity o

f Wes

tern

Ont

ario

on

02/0

5/15

. For

per

sona

l use

onl

y.


98. de la Paz ML, Serrano L. 2004. Sequence determinants of amyloid bril formation. Proc. Natl. Acad. Sci.USA 101:8792

99. de la Paz ML, Goldie K, Zurdo J, Lacroix E, Dobson CM, et al. 2002. De novo designed peptide-basedamyloid brils. Proc. Natl. Acad. Sci. USA 99:1605257

100. Mehta AK, Lu K, Childers WS, Liang Y, Dublin SN, et al. 2008. Facial symmetry in protein self-assembly. J. Am. Chem. Soc. 130:982935

101. Balbach J, Ishii Y, Antzutkin O, Leapman R, Rizzo N, et al. 2000. Amyloid bril formation by A1622,a seven-residue fragment of the Alzheimers-amyloid peptide, and structural characterization by solidstate NMR. Biochemistry 39:1374859

102. Tjernberg LO, Naslund J, Lindqvist F, Johansson J, Karlstrom AR, et al. 1996. Arrest of -amyloidbril formation by a pentapeptide ligand. J. Biol. Chem. 271:854548

103. Ricchiuto P, Brukhno AV, Auer S. 2012. Protein aggregation: kinetics versus thermodynamics. J. Phys.Chem. B 116:538490

104. Hoang TX, Trovato A, Seno F, Banavar JR, Maritan A. 2004. Geometry and symmetry presculpt thefree-energy landscape of proteins. Proc. Natl. Acad. Sci. USA 101:796064

105. Meral D, Urbanc B. 2013. Discrete molecular dynamics study of oligomer formation by N-terminallytruncated amyloid -protein. J. Mol. Biol. 425:226075

106. UrbancB, BetnelM,CruzL,LiH, FradingerE, et al. 2011. Structural basis forAC-terminal fragments:discrete molecular dynamics study. J. Mol. Biol. 410:31628

107. Urbanc B, Betnel M, Cruz L, Bitan G, Teplow D. 2010. Elucidation of amyloid-protein oligomeriza-tion mechanisms: discrete molecular dynamics study. J. Am. Chem. Soc. 132:426680

108. Peng S, Ding F, Urbanc B, Buldyrev S, Cruz L, et al. 2004. Discrete molecular dynamics simulations ofpeptide aggregation. Phys. Rev. E 69:041908

109. Ding F, Furukawa Y, Nukina N, Dokholyan NV. 2012. Local unfolding of Cu, Zn superoxide dismutasemonomer determines the morphology of brillar aggregates. J. Mol. Biol. 421:54860

110. Redler RL, Wilcox KC, Proctor EA, Fee L, Caplow M, Dokholyan NV. 2011. Glutathionylation atCys-111 induces dissociation of wild type and FALS mutant SOD1 dimers. Biochemistry 50:705766

111. Cote S, Laghaei R, Derreumaux P, Mousseau N. 2012. Distinct dimerization for various alloforms ofthe amyloid- protein: A140, A142, and A140 (D23N). J. Phys. Chem. B 116:404355

112. Spill YG, Pasquali S, Derreumaux P. 2011. Impact of thermostats on folding and aggregation propertiesof peptides using the optimized potential for efcient structure prediction coarse-grainedmodel. J. Chem.Theory Comput. 7:150210

113. Chebaro Y, Jiang P, Zang T, Mu Y, Nguyen PH, et al. 2012. Structures of A1742 trimers in isolationand with ve small-molecule drugs using a hierarchical computational procedure. J. Phys. Chem. B116:841222

114. Lu Y, Wei G, Derreumaux P. 2012. Structural, thermodynamical, and dynamical properties of oligomersformed by the amyloid NNQQ peptide: insights from coarse-grained simulations. J. Chem. Phys.137:025101

115. Nasica-Labouze J, Meli M, Derreumaux P, Colombo G, Mousseau N. 2011. A multiscale approach tocharacterize the early aggregation steps of the amyloid-forming peptide GNNQQNY from the yeastprion Sup-35. PLoS Comp. Biol. 7:e1002051

116. Nasica-Labouze J, Mousseau N. 2012. Kinetics of amyloid aggregation: a study of the GNNQQNYprion sequence. PLoS Comput. Biol. 8:e1002782

117. Laio A, Parrinello M. 2002. Escaping free-energy minima. Proc. Natl. Acad. Sci. USA 99:1256266118. Gronau G, Qin Z, Buehler MJ. 2013. Effect of sodium chloride on the structure and stability of spider

silks N-terminal protein domain. Biomater. Sci. 1:27684119. Camilloni C, Schaal D, Schweimer K, Schwarzinger S, De Simone A. 2012. Energy landscape of the

prion protein helix 1 probed by metadynamics and NMR. Biophys. J. 102:15867120. Rossetti G, Cossio P, Laio A, Carloni P. 2011. Conformations of the Huntingtin N-term in aqueous

solution from atomistic simulations. FEBS Lett. 585:308689121. Wang H, Barreyro L, Provasi D, Djemil I, Torres-Arancivia C, et al. 2011. Molecular determinants and

thermodynamics of the amyloid precursor protein transmembrane domain implicated in Alzheimersdisease. J. Mol. Biol. 408:87995



Ann

u. R

ev. P

hys.

Chem

. 201

5.66

. Dow

nloa

ded

from

ww

w.an

nual

revi

ews.o

rg A

cces

s pro

vide

d by

Uni

vers

ity o

f Wes

tern

Ont

ario

on

02/0

5/15

. For

per

sona

l use

onl

y.


122. Torrie GM, Valleau JP. 1977. Nonphysical sampling distributions in Monte Carlo free-energy estima-tion: umbrella sampling. J. Comput. Phys. 23:18799

123. Rivera E, Straub J, Thirumalai D. 2009. Sequence and crowding effects in the aggregation of a 10-residuefragment derived from islet amyloid polypeptide. Biophys. J. 96:455260

124. Davis C, Berkowitz M. 2009. Interaction between amyloid- (142) peptide and phospholipid bilayers:a molecular dynamics study. Biophys. J. 96:78597

125. Sugita Y, Okamoto Y. 1999. Replica-exchange molecular dynamics method for protein folding. Chem.Phys. Lett. 314:14151

126. Sugita Y, Kitao A, Okamoto Y. 2000. Multidimensional replica-exchange method for free-energy calcu-lations. J. Chem. Phys. 113:604251

127. Fukunishi H, Watanabe O, Takada S. 2002. On the Hamiltonian replica exchange method for efcientsampling of biomolecular systems: application to protein structure prediction. J. Chem. Phys. 116:905867

128. Ostermeir K, Zacharias M. 2013. Advanced replica-exchange sampling to study the exibility and plas-ticity of peptides and proteins. Biochim. Biophys. Acta 1834:84753

129. Kim J, Straub JE,KeyesT. 2012. Replica exchange statistical temperaturemolecular dynamics algorithm.J. Phys. Chem. B 116:864653

130. Kim J, Straub JE, Keyes T. 2006. Statistical-temperature Monte Carlo and molecular dynamics algo-rithms. Phys. Rev. Lett. 97:050601

131. SwendsenRH,Wang JS. 1986.ReplicaMonteCar

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