Interaction of Amyloid Inhibitor Proteins with Amyloid Beta Peptides: Insight from Molecular Dynamics Simulations

Knowledge of the detailed mechanism by which proteins such as human αB- crystallin and human lysozyme inhibit amyloid beta (Aβ) peptide aggregation is crucial for designing treatment for Alzheimer's disease. Thus, unconstrained, atomistic molecular dynamics simulations in explicit solvent have been performed to characterize the Aβ17–42 assembly in presence of the αB-crystallin core domain and of lysozyme. Simulations reveal that both inhibitor proteins compete with inter-peptide interaction by binding to the peptides during the early stage of aggregation, which is consistent with their inhibitory action reported in experiments. However, the Aβ binding dynamics appear different for each inhibitor. The binding between crystallin and the peptide monomer, dominated by electrostatics, is relatively weak and transient due to the heterogeneous amino acid distribution of the inhibitor surface. The crystallin-bound Aβ oligomers are relatively long-lived, as they form more extensive contact surface with the inhibitor protein. In contrast, a high local density of arginines from lysozyme allows strong binding with Aβ peptide monomers, resulting in stable complexes. Our findings not only illustrate, in atomic detail, how the amyloid inhibitory mechanism of human αB-crystallin, a natural chaperone, is different from that of human lysozyme, but also may aid de novo design of amyloid inhibitors.


Introduction
Alzheimer's disease (AD) is the most common form of dementia affecting nearly 38 million people worldwide. The pathological hallmarks of AD are the aberrant Data Availability: The authors confirm that all data underlying the findings are fully available without restriction. All relevant data are within the paper and its Supporting Information files.
Funding: This work was funded by IBM BlueGene Science Program. The funder provided support in the form of salaries for authors [PD], but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the 'author contributions' section. GB acknowledges support from New York Capital Alliance RPI # J50552. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: This work was supported by the IBM Blue Gene Science program. Co-authors Payel Das and Seung-gu Kang are affiliated with IBM Research. There are no patents, products in development or marketed products to declare. This does not alter the authors' adherence to all the PLOS ONE policies on sharing data and materials. deposition of extracellular senile plaques comprised of amyloid-beta (Ab) peptides and intracellular neurofibrillary tangles [1]. Ab isoforms of different lengths (ranging from 38 to 43) are generated by sequential cleavage of the amyloid precursor protein (APP) via proteolytic processing. Ab40 and Ab42 are the major isoforms generated via the ''amyloidogenic'' pathway by band csecretase. In addition, the Ab 17-40/42 fragments known as the p3 peptides are generated via ''non-amyloidogenic'' pathway by aand c-secretase.
The abnormal aggregation of the Ab peptides into b-sheet rich fibrils involves a heterogeneous ensemble of oligomeric intermediates, all of which are found to be neurotoxic [2]. Ab toxicity likely originates from a number of factors, including formation of ion channels [3], oxidative stress [4], interaction with receptors [5]. A recent study reported that the p3  peptides undergo faster aggregation in vitro compared with Ab 1-42 peptides, while the fibril morphology and the oligomerization remain unaltered [6]. NMR data for the Ab fibril structure proposed either parallel or anti-parallel orientations of the b-sheets [7]. Additional NMR studies [8][9][10][11] suggested Ab 1-42 fibril models as parallel-stacked hairpin-like structures of Ab peptides. Residues 1-9/17 appear unstructured, whereas residues 18-42 form a b-strand-turn-b-strand hairpin motif that comprises two intermolecular, parallel, in-register b-sheets formed by residues 18-26 and 31-42. Meanwhile, other proteins such as small heat shock proteins (sHsps) are also found co-localized with Ab peptides in the amyloid plaque [12][13][14]. One of sHsps, aB-crystallin, has been extensively studied. aB-crystallin acts as an archetypical and ubiquitous ATP-independent molecular chaperone that binds partially unfolded polypeptides and maintains them in a refolding-competent state [15][16][17]. aB-crystallin is present in many parts of the human body including skeletal muscles and heart, and is a crucial component of the eye lens [18]. The native monomer of the aB-crystallin (,175 residues) comprises a ,90 residue b-sandwich domain that is termed the a-crystallin domain (ACD) and is highly conserved among all sHsps [19] (Fig. 1a & 1c). ACD is flanked by a variable, largely unstructured N-terminal region and a moderately conserved C-terminal extension [20]. It forms stable dimers that further assemble into a heterogeneous mixture of larger homo-oligomers [21]. Experiments suggest that ACD possesses considerable chaperone activity as well as contains interactive sequences against substrate proteins [22][23][24][25].
aB-crystallin is up-regulated in the brain of AD patients [13] and is also associated with Ab deposition in the supranuclear cataract of the lenses of AD patients [26]. The fact that aB-crystallin is found co-localized with Ab in vivo has stimulated in vitro experiments [27][28][29][30][31][32][33][34] to understand the effect aB-crystallin on Ab aggregation. A majority of these experiments suggest that aB-crystallin can inhibit Ab amyloid fibril formation by direct binding [30][31][32] and has an inhibitory effect on Ab-associated toxicity and aggregation [29,30,35,36]. Dobson and coworkers have found that aB-crystallin tightly binds with Ab oligomers, thereby inhibiting their conversion to fibrils as well as their interaction with membrane [33,34], which might help modulating the Ab-mediated toxicity [37].
Interestingly, several other proteins that are not molecular chaperone have been reported to retard Ab fibril formation as well [38]. For example, human lysozyme has been shown to inhibit Ab aggregation in vitro at higher stoichiometric ratios than aB-crystallin [39]. The sequence, structure and the protein surface amino acid composition distinctively differ between lysozyme and ACD. Lysozyme is a primarily helical protein with a net +8 charge at pH 7 (see Fig. 1b & 1c). On the other hand, ACD shows a b-sandwich fold and has net charge of -2 ( Fig. 1a). At present, limited data on the interaction between Ab peptides and these amyloid (a) Structure of an ACD monomer in cartoon and of the ACD dimer in surface representation colored according to residue type. Color scheme used: red -acidic, blue -basic, green -polar, and white -hydrophobic. (b) Cartoon and surface representations of the human lysozyme protein colored according to the residue type. (c) Sequence and the secondary structure assignment of human acrystallin domain (ACD, residues 66-150) and of human lysozyme using the secondary structure assignment program DSSP [97]. Yellow arrows indicate bstrands, purple indicates turn, blue indicates bend, red spirals indicate the alpha-helix, light pink spirals indicate the 3 10 helix, and black indicates coils. Sequence of the Ab 17-42 peptide is also shown. (d) System set up with one ACD dimer (black cartoon) placed in the center of a cubic box of water (shown in red) that also contains 10 Ab 17-42 peptides (green spheres, only backbone is shown). Sodium and Chloride ions are shown as cyan and yellow spheres, respectively.
doi:10.1371/journal.pone.0113041.g001 inhibitor proteins exists, which is needed for designing novel protein therapeutics for AD.
Since most experimental approaches do not have the necessary resolution to determine inhibitor-peptide binding interactions at an atomic level, molecular dynamics (MD) simulations provide an alternative approach for such problem. MD simulations have been widely used to complement experiments [40] in providing detailed information on the structure of various Ab species ranging from monomers [41][42][43][44][45] to oligomers [46,47] to protofibrils [48] to fibrils [49]. Interactions of different Ab species with toxicity and aggregation inhibitors [50][51][52] and with lipid bilayers [53][54][55] have been also studied using MD.
In the present study, unconstrained, atomistic MD simulations in explicit water are employed to characterize the effect of the structured core domain of aB-crystallin as well as of lysozyme on the assembly of Ab  peptides and the interaction between them (Fig. 1d). The choice of the Ab17-42 fragment is motivated by several reasons: (1) the naturally occurring ''amyloidogenic'' 17-42 fragments of Ab, known as the p3 peptides, which are constituents of AD amyloid plaques [56] and cerebellar pre-amyloid lesions in Down's syndrome [57], induce neuronal toxicity characteristic of AD [58], and form ion channels [59]. Recently, a crystal structure of the p3 fragment has been reported, providing a model for non-fibrillar Ab oligomers [60]. (2) Those N-terminally truncated peptides are found to aggregate profoundly in in vitro experiments [6]. (3) The 17-42 fragment is comprised of the two hydrophobic patches (L17-A21 and A30-A42) and the turn region (E22-G29) that are crucial for determining aggregation and toxicity, form the strand-loop-strand conformation in fibrils, and also contain the vast majority of disease-causing mutations. (4) Ab fragments have been the subject of many MD simulations in explicit water to offer useful atomistic information [42,61,62] [51,63]. Finally, the N-terminal truncation lowers the computational expense significantly and allows us to obtain reliable statistics. Our simulations reveal distinct preference of individual inhibitor protein for binding to peptide monomers vs. oligomers. The molecular factors underlying such differences in the Ab binding dynamics are further illustrated in detail.

Effect of ACD and lysozyme binding on Ab assembly
To study in detail the effect of the structured core domain (ACD) of a human aB-crystallin dimer and of a human lysozyme molecule on the Ab 17-42 assembly, we performed an aggregate of ,4.5 ms of unconstrained, explicit solvent, atomistic MD. Due to limited available information on the putative Ab binding modes with ACD and with lysozyme, brute force MD was used. We placed ten peptides randomly in the simulation box to explore multiple binding sites on inhibitors and their preference for peptide monomers vs. oligomers. A much higher Ab concentration compared to experiments was used to expedite the association kinetics in simulations, while keeping the inhibitor:peptide ratio at 1:10, which is close to experiments (see Model and Method section). Three systems were simulated: (i) ten peptides as a control system, (ii) ten peptides and one ACD dimer, and (iii) ten peptides + one lysozyme molecule. At least five different §200 ns runs were performed for each system at 325 K and 1 atm.
To probe the competition between the peptide-peptide and peptide-inhibitor binding during the very early-stage (,200 ns) of aggregation, we computed the two-dimensional potential of mean force plots as a function of (i) the number of contacts between the inhibitor and a peptide, and (ii) the number of contacts between a peptide and all other peptides (Fig. 2). ACD-complexed Ab oligomers appear prevalent, as indicated by the higher probability of the configurations containing significant number of ACD-Ab and inter-peptide contacts (Fig. 2a). A minor (1%) population of ACD-bound monomers is also noticed, as represented by the region on the PMF plot with number of ACD-Ab number of contacts being >5 and number of inter-peptide contacts being ,5. In contrast, lysozyme preferentially binds to peptide monomers, suggested by the dominant population of lysozyme-bound peptides that form limited contacts with other peptides (Fig. 2b). However, a smaller (4%) population with strong lysozyme-peptide binding (number of lysozyme-Ab contacts.40) is also noticed, which also interact with other peptides (number of Ab-Ab contacts.40). Such population is not observed in the ACD case (see below).
These results are further confirmed by computing average number of different sized inhibitor-bound Ab species at different time interval and comparing that with the results obtained for the control system (Fig. 2c). Results for all individual runs are found in the supplementary information ( Fig. S1-S3 in File S1). We considered monomers, small oligomers (n52-5) and larger oligomers (n.5) separately in this analysis. Figure. 2c reveals that the monomers and small oligomers are the prevalent species during the ,200 ns simulation of control system (top panel). In presence of ACD, during the first 50 ns the number of complexed monomers and complexed small oligomers appear nearly the same (Fig. 2c, middle). As the simulation progresses, the number of ACD-bound monomer becomes lower with increasing presence of ACD-complexed small oligomers. The complexed oligomers remain present during rest of the simulation. Some population of larger complexed oligomers is also observed after 100 ns.
In contrast, peptide monomers dominate in lysozyme binding, as the monomers appear to be the prevalent complexed species (Fig. 2c, bottom). The population of small complexed oligomers remains constantly smaller than complexed monomers in presence of lysozyme. Figure 2c further indicates that the number of lysozyme-complexed monomers is higher compared with the ACD-bound ones during the total time-course of simulation. These results suggest that both inhibitors compete with the inter-peptide interaction by binding to the peptides. Such complexation would lower the effective concentration of the free peptides in solution, contributing to aggregation inhibition, which matches closely with experiments [31,35,36,39]. However, the inhibition mechanism varies depending on the presence of ACD or lysozyme. For the ACD case, sequestration of the free small oligomers is observed, while monomers are primarily sequestered in presence of lysozyme.

ACD-Ab contact surface is less extensive
To compare the inhibitor-peptide and inter-peptide interaction, we computed the probability distribution of the number of contacts for the inhibitor-complexed monomers (ACD and lysozyme), complexed oligomers (ACD-bound only), and free oligomers (Fig. 3a). The complexes that have more than five heavy atom contacts were only considered for this analysis. The ACD-peptide monomer interaction appears weakest, as suggested by the peak location of the distribution. When a peptide from an Ab oligomer binds to ACD, the ACD-Ab interaction surface appears relatively more extensive compared to the scenario of a single monomeric peptide bound to ACD (indicated by the higher probability of forming more than ten contacts). In contrast, lysozyme-peptide binding appears nearly comparable to the inter-peptide binding in terms of the number of contacts (Fig. 3a). Consistently, the rate of decrease of the time-dependent survival probability shows the following order: ACD-bound monomer ,ACD-bound oligomer ,lysozyme-bound monomer (Fig. 3b). The evolutions of the number of complexed peptide monomers and oligomers during a typical trajectory show similar trend (Fig. S4 in File S1). ACD first encounters with an Ab monomer (t,25 ns), which dissociates shortly ( Fig. S5a in File S1). In the later stage (t5,50 ns), one Ab dimer and one Ab trimer form complexes with ACD ( Fig.  S4a in File S1). Once formed, these ACD-bound small Ab oligomers (one dimer and one trimer) remain attached for ,100 ns. In contrast, during a typical trajectory amyloid monomers bind first with lysozyme ( Fig. S4b in File S1). Over time, these complexed monomers can assemble to form complexed higher order aggregates (populating the upper right region of Fig. 2b). Taken together, these results suggest that the Ab monomers make limited contacts with ACD, resulting in transient complex formation. The small oligomers, however, can form relatively more stable complexes with ACD by making higher number of contacts. The more stable interaction of an Ab oligomer with ACD is due to the simultaneous contact formation of more than one monomer. It is also possible that the slower reconfiguration time [64] of the oligomer (compared with the monomer) allows more extensive interaction with ACD. In contrast, lysozyme interacts strongly with monomeric peptides, which is comparable to the inter-peptide surface, resulting in longer-lived complexes. (a) Probability distributions of the number of heavy atom contacts formed between two Ab peptides (black) in the control system (no inhibitor), between ACD and an Ab monomer (red), between ACD and an Ab oligomer (green), and between lysozyme and an Ab monomer (blue). Lysozyme-bound Ab oligomers were excluded from the analysis due to their minor population. At least five different ,200 ns runs were used, in which multiple binding/unbinding events were observed. (b) Mean survival time correlation function, S(t), of peptides in the vicinity of the inhibitor: ACD-bound monomer (black), ACD-bound oligomer (red) and lysozyme-bound monomer (green). Each curve shows average of five independent runs. S(t50) measures the average number of peptide molecules bound with inhibitor, and S(t) gives the average number of peptide molecules that remain bound after a period of time, t, given that they were present at t50. A short escape of 1 ns was allowed during the calculation.

Specific binding interactions of Ab peptides with inhibitors
Why ACD-peptide binding is less extensive than the inter-peptide binding, whereas the opposite effect is observed for lysozyme? To answer this question, we compared the binding interactions of Ab peptides with ACD and with lysozyme by estimating their ensemble-averaged relative contact probabilities (Fig. 4). Two distinct regions of the crystallin domain are primarily found to interact with Ab ( Fig. 4a-b); (i) the b4-b8 pocket and (ii) the top b-sheet (b2, b3 and b9 strands). Previous studies suggest that these regions comprise many surface-exposed residues that are implicated in substrate binding [65]. The buried ACD dimer interface comprising the b6+7 strands lacks interaction with amyloid peptides, as expected ( Fig. 4a-b). From the peptide side, both termini tend to interact with ACD. Only a few contacts are observed in the middle turn region (residues 24-29) except for K28. Consistently, the highly probable ACD-Ab residue pairs include L131-V40, T132-V40, R149-I41, R74-E22, R107-E22, and E105-K28.
Similar analysis of the lysozyme-Ab interaction shows that arginines from lysozyme that are dominate binding with the Ab peptide (Fig. 4c-d). In fact, arginines are prevalent in lysozyme sequence (14 in total). Residues with high Ab contacting probability include R14, R21, R101, R115, R119, and R122, which are all located within the alpha-domain (Fig. 4d). Some additional contacts with proximal hydrophobic (Y20, W34) and polar (Q123 and Q126) residues are also observed (Fig. 4d). Consistently, the highly probable contacts involve residues R21, R101, and R119 from lysozyme and residues E22, D23, and A42 (with negatively charged C-terminus) from Ab.
The contact probability per amino acid type analysis (Fig. 4e) reveals that both positively and negatively charged residues (Arg, Lys, Glu) of ACD dominate Abbinding, while significant participation of the polar (Ser, Thr), and hydrophobic (Leu, Pro, Val) residues is also observed. These results imply that the ACD contact surface is more heterogeneous in terms of the amino acid composition, as no particular amino acid type shows a strong binding preference for Ab. This result is consistent with the heterogeneous sequence distribution of the ACD surface (Fig. 1a). We further estimated the residue-specific contact probability of Ab (Fig. 4f). L17, F20, E22, K28, and the carboxyl-terminated C-terminus ( 39 VVIA 42 ) from Ab often contact ACD. The higher contact probability of the mainly hydrophobic C-terminus is consistent with their frequent interaction with the b4, b8, and b9 strands of ACD (Fig. 4a). Given the more heterogeneous nature of the ACD surface, it is likely difficult for the Ab N-terminus (+NH 3 -17 LVFFAED 23 ) to find a complementary binding pocket that can satisfy all or majority of the possible charge-charge interactions. Thus, the C-terminus (with a smaller local concentration of charged residues) appears to remain in contact with ACD more frequently compared to the N-terminus. The more heterogeneous ACD surface also explains why a single Ab monomer is less likely to form an extensive contact surface with ACD (in contrast to what observed with lysozyme, Fig. 2-3) and thus is not stable, which lead to ACD's preference for the peptide oligomers.
In contrast, arginines from lysozyme alone control the binding with Ab (Fig. 4e). Much stronger participation from the Ab N-terminus (mainly near the acidic residues) is noticed in lysozyme binding compared to that observed for ACD binding, suggesting that attractive electrostatic forces dominate lysozyme-Ab interaction. The C-terminus and residues 34-38 also exhibit high contact probability. The high lysozyme-contacting probability of several Ab residues is consistent with a more extensive contact surface (Fig. 3a). Overall, the arginines in the alpha-domain of lysozyme drives formation of a stable, extensive contact surface with the negatively charged residues of the Ab peptides in their monomeric form, which is further accompanied by a few hydrophobic and polar contacts. Such extensive interaction allows lysozyme to compete more efficiently with the inter-peptide interaction compared with that for ACD.
Given the importance of the D23-K28 salt-bridge in maintaining the rigidity of the hairpin-like monomeric structure in the oligomers [66] and fibrils [8,11], we further evaluate the interaction of those two residues (D23 and K28) with the two inhibitor proteins. Overall, K28 shows a ,40% contact probability with ACD and contacts strongly with E105, E106, T134, and S135. D23 interacts with ACD with ,30% probability, particularly with K74, T134, and N146. On the other hand, residues E102, N104, and N118 from lysozyme contact with K28 of Ab that shows an overall contact probability of 40%. D23 of Ab strongly contributes to lysozyme binding (with 100% probability) and contacts with W34, R119, R122, and Q126. In summary, both inhibitor proteins strongly engage residues D23 and K28 of Ab via electrostatic interactions.

ACD and lysozyme remain structurally intact upon Ab binding
Next, we investigated if the inhibitors undergo any structural change upon Ab binding or not. The evolutions of the root-mean-square distance (RMSD) from the native structure show that both ACD and lysozyme remain quite stable over the simulation time (Fig. S5a in File S1). Lysozyme appears relatively more stable with RMSD fluctuating around 1.5 Å . The RMSD of crystallin domain fluctuates between 2 and 4 Å . The root-mean-square-fluctuation (RMSF) per residue plot (Fig. S5b in File S1) demonstrates that all secondary structure elements of crystallin domains remain unperturbed upon Ab interaction, while the loops connecting the strands fluctuate. These results are consistent with the reported high stability of the ACD dimer observed in chemical denaturation experiments [67] and also with the hyperthermophilic nature of this protein. For lyszoyme, only a5 and a7 helices exhibit RMSF values higher than 1.5 Å , while the rest of the secondary structural elements remain highly intact (Fig. S5b in File S1). Overall, the results imply that both inhibitors remain structurally unperturbed upon peptide binding.

Effect of inhibitor binding on the Ab conformation
We further analyzed the effect of inhibitor binding on the structure of Ab peptides. For this purpose, an ensemble consisting of .10,000 peptide structures were used for each case. A peptide is considered to be complexed, if it forms more than five contacts with ACD/lysozyme. The secondary structure (Fig. S6 in File S1) as well as the tertiary and quaternary contact probabilities (Fig. 5) were estimated. The ensemble-averaged secondary structure propensity (Fig. S6a in File S1) of the peptides in the control system reveals that coils and turns dominate at ,33% and ,55%, respectively, suggesting a mainly unstructured Ab  . This finding is consistent with earlier replica-exchange simulations of Ab 17-42 [68]. Similar results are found for the complexed peptides, suggesting insignificant secondary structure change upon inhibitor binding. Some transient a-helix formation is noticed in the C-terminal region of Ab upon ACD interaction (Fig.  S6b in File S1).
The tertiary contact probability plot for the free peptides suggests substantial short-range interactions along the sequence (Fig. 5a). Residues 18-20 from CHC form weak, long-range, hydrophobic contacts with residues 30-40, especially with L34 and M35 (with a probability of ,35%), similar to that reported for the hairpin-like conformation in the NMR-based fibril structure [9,10]. Upon ACD binding, the tertiary structure of Ab shows some changes. Short-range interactions, especially those near residues K28 and in the C-terminus (residues Figure 5. Probability of peptide-peptide contact formation. Ensemble-averaged probabilities of (a) tertiary contact and (b) quaternary contact formation of Ab peptides in the control system (left), ACD-bound (middle), or lysozyme-bound (right) obtained from an ensemble generated from at least five ,200 ns runs. The size of the ensemble is.10000 conformations. The peptide is considered complexed, if it forms more than five contacts with ACD/lysozyme. Only the non-sequential tertiary contacts (that are not formed between neighboring residues (i+1, and i+2) in sequence) are shown. The contacts are color-coded according to the color scale shown on the right. Snapshots of the oligomeric conformations with prevalent inter-monomer contacts are shown at bottom. Peptides are colored in green, pink, or tan, whereas ACD/lysozyme is colored in white. The N-and C-termini of the peptides are colored in red and blue, respectively. For the ACD-bound oligomer, only the inter-peptide contacts that form with higher probability compared to the free oligomer are shown for clarity.
doi:10.1371/journal.pone.0113041.g005 [32][33][34][35][36][37][38], become stronger upon ACD interaction, consistent with observed transient a-helix formation in this region (Fig. S6b in File S1). In the lysozymebound peptides, residues 19-21 show slightly higher contact probabilities with residues 29-32 and residues 39-41, when compared with the free peptides. In addition, lysozyme binding also induces local interaction within the peptide, but to a lesser extent to that seen for the ACD-bound peptide. Figure 5b shows the quaternary contact probability plots for Ab peptides. Results for the free peptides reveal that all regions except residues 21-23 and 25-29 are involved in the inter-peptide association, with residues 31-35 showing relatively higher tendency. These results are in overall good agreement with earlier experimental [69] and simulation results [70], suggesting the importance of these hydrophobic regions in inter-peptide interaction. Upon complexation with ACD, hydrophobic residues from the N-terminus (e.g. residues F19, and F20) and from the C-terminus (e.g. residues L34 and M35) show enhanced propensity to interact with other peptides. Figure 5b shows snapshots of these oligomers with hydrophobic contacts formed at the inter-monomer interface. In contrast, very few inter-peptide contacts appear in lysozyme-complexed peptides, suggesting that the extensive lysozyme-Ab monomer attraction does not allow formation of the hydrophobic inter-monomer interface. Thus, the inter-peptide contact appears limited upon lysozyme binding.

Discussion and Conclusion
Several studies have suggested that aB-crystallin can protect the cell from Ab aggregation and toxicity at sub-stoichiometric ratios [31,35,36]. Single-molecule experiments performed at an equimolar ratio also suggested formation of stable complexes between aB-crystallin and small Ab 1-40 aggregates (n52-10) during disaggregation reaction [33]. Recently, a designed dimer consisting only the acrystallin domain has been shown to act as a potent inhibitor of amyloid fibril formation and toxicity [25], which is very similar to our simulated system of ACD dimer. Separately, human lysozyme, which is not a chaperone, can completely inhibit Ab aggregation at equimolar lysozyme: Ab 1-40 ratio [39]. The same study reported lag time delays of Ab peptide aggregation at 1:10 ratio of lysozyme and peptide. In line with these experiments, the current study shows that both lysozyme and the ACD dimer inhibit early oligomerization of Ab 17-42 peptides at 1:10 ratio by competing with inter-peptide interaction. However, the simulations indicate that the mechanisms by which a-crystallin domain and lysozyme interact with Ab 17-42 are quite different. Ab monomers bind with ACD via limited interactions due to the more heterogeneous nature of the ACD surface. The resulting complexes are transient. Nevertheless, small Ab oligomers form more stable complexes with ACD, as the peptides can collectively form higher number of contacts with ACD. These ACD-bound peptides also demonstrate stronger inter-peptide hydrophobic contacts. Thus, the ACD-bound oligomers remain stable for ,100 ns. Mainly charged residues as well as some hydrophobic and polar residues from the top b-strands and the b4-b8 pocket of ACD participate in Ab-binding.
It should be mentioned that the flanking regions of ACD (the variable, largely unstructured N-terminal region and the moderately conserved C-terminal extension) [20] are not included in our simulations. It is likely that those flanking regions, particularly the 65 residue long N-terminal region, also contribute to Ab binding. Several studies suggest various binding sites within aB-crystallin, which include both ACD and the flanking regions, but there is little agreement [24,35,71,72]. In the present study, those flanking disordered regions are not included in the model to keep the computational expense reasonable. It should be also mentioned that, ACD alone, in both monomeric and dimeric forms, is sufficient for inhibiting Ab 42 aggregation and toxicity [25], which supports the relevance of our simulations in understanding the amyloid inhibitor activity of aB-crystallin.
In contrast, human lysozyme can form a large number of attractive electrostatic interactions due to the prevalent presence of locally concentrated arginines on its surface. Consequently, lysozyme can simultaneously bind with multiple Ab monomers and form longer-lived complex with them. These results emphasize the importance of the surface composition of an inhibitor protein in determining the details of the molecular mechanism of amyloid inhibition. In addition, these simulations highlight the importance of the electrostatics in the Ab-inhibitor interaction, consistent with recent experiments [38].
Interestingly, Ab monomers have been reported to be neuro-protective [73,74], whereas the small oligomers (n52-4) as well as dodecamers and protofibrils are associated with neurotoxicity [75][76][77], indicating a ''loss of function'' by pathological aggregation of Ab peptides. In addition, small oligomers (n52-4) are efficient in nucleating assembly; trimer and tetramer being more efficient than the dimer [78]. Experiments show that the toxic Ab 1-42 oligomers maintained their toxicity in presence of hen egg white lysozyme that shares a very high structural (RMSD50.65 Å ) and sequence similarity (61%) with human lysozyme; however, the toxicity was significantly reduced in presence of aB-crystallin [37]. More recent experiments indicate that human lysozyme suppresses Ab 1-40 aggregation and also to some extent toxicity at a 1:1 molar ratio [79]. Taken together, previous experiments [30,31,36,37,39] suggest that natural chaperones that are of direct biological relevance, such as aB-crystallin, can exhibit an inhibitory effect on both Ab aggregation and toxicity at greatly sub-stoichiometric concentrations. In contrast, human lysozyme, a non-chaperone protein, can inhibit Ab aggregation and to some extent toxicity at much higher stoichiometric concentrations [79]. A non-specific binding between lysozyme and random coil Ab monomers with some hydrophobic contribution was also suggested [79], which is overall in good agreement with our results. The findings of this study further imply that the molecular chaperone is naturally designed to inhibit amyloid aggregation by preferentially forming stable complexes with small oligomers (as opposed to a non-chaperone protein binding to monomers), which is determined by its heterogeneous surface composition. We hypothesize that the natural preference of the molecular chaperones for smaller amyloid oligomers may help optimizing their protective action. Overall, we present a dynamic molecular picture of the Ab peptides interacting with two amyloid inhibitors by using atomistic simulations, which may serve to guide the rational design of more effective chaperones and amyloid inhibitors.

Model and Method
The initial structure of a dimer of the a-crystallin domain (ACD) (Fig. 1a) was taken from the crystal structure deposited in the Protein Data Bank (residues 66-150 from PDB ID code 2wj7) [80]. The ACD forms an immunoglobin-like b-sandwich fold comprising strands b2-b9, and the assembly unit is a dimer (Fig. 1a). The initial coordinates of the monomeric Ab 17-42 was obtained from the NMR structure of the Ab 1-42 fibrils (PDB ID code 2beg). The protonation state of the peptide was set to that at pH 7 for all simulations. The ACD dimer was placed in the center of a ,124 Å 6124 Å 6124 Å 3 cubic box of water containing 100 mM NaCl to closely mimic physiological conditions. Ten Ab 17-42 peptides with charged termini were placed in random orientation at the center of the faces and at alternating vertices of the cubic box. This results in the simulated concentration of ,8.7 mM Ab that is much higher than what is typically used in experiments (,10-50 mm) [30,31,36]. Thus, a much higher Ab concentration compared to the experiments was used to expedite the association kinetics in simulations by reducing the time for random diffusion.
The minimum distance (only considering heavy atoms) between the ACD dimer and Ab peptide was set to 15 Å . Ions were added to neutralize the net charge of the system (-2e for each ACD domain, -1e for Ab . Figure 1d illustrates one typical system of the solvated system with ten Ab peptides and one ACD dimer. This system, consisting of a total of ,180,000 atoms, was first energy-minimized for 50,000 steps followed by a 1 ns equilibration with a 0.5 fs time step. At least five different MD runs were performed at 325 K and 1 atm for each of the three systems starting from the equilibrated structure: (i) the control system containing ten peptides (,164,000 atoms in a 12061206120 Å 3 cubic box), (ii) ten peptides and one ACD dimer (,180,000 atoms in a 12461246124 Å 3 cubic box), and (iii) ten peptides and one lysozyme molecule (,164,000 atoms in a 12061206120 Å 3 cubic box). The system containing one lysozyme molecule and ten peptides was prepared following a similar protocol, in which one human lysozyme molecule (residues 1-130, PDB ID code 1rex, +8e charge) was placed in the center of the simulation box. Each simulation was started from different initial coordinates and velocities assigned from a Maxwell-Boltzmann distribution at the specified temperature. The initial orientation of the ACD dimer (or lysozyme) and the initial location of the peptides in the box were different in each run to remove bias of the initial structure on the final results. To rule out the possibility that the initial coordinates of the Ab peptides taken from a fibril structure might affect our final conclusions, we plotted the evolutions of the C a -RMSD of all ten peptides from the initial structure during the first 10 ns of MD of the control system in Fig.  S7 in File S1. Within first 4-5 ns, the C a , RMSD of those peptides reaches a value of 6-10 Å , consistent with their disordered nature. This result confirms that our conclusions are independent of the choice of the Ab initial coordinates. The simulations were performed for 200 ns or longer. The total aggregate simulation time was ,4.5 ms.
The relative concentrations of ACD and Ab are similar to that used in experiments, in which aB-crystallin are found to interact with Ab variants and inhibit their aggregation and toxicity [30,31,36,37]. Use of multiple peptides in the simulation system allows exploration of more than one binding sites on the inhibitor proteins as well as their interaction preference for peptide monomers vs. oligomers. It should be noted that exact size prediction of the inhibitorcomplexed oligomers is beyond the scope of this study and thus the size reported here should be considered in a more qualitative manner. The exact size of the complexed oligomers can be affected by several factors such as the finite size of the system, simulation timescale, and the relative concentration of inhibitor and peptides.
The particle-mesh Ewald (PME) method was used for the long-range electrostatic interactions [81], while the van der Waals interactions were treated with a cut-off distance of 12 Å . The CHARMM22 [82] force field with CMAP extension [83] was used for the proteins. This force-field has been widely used to simulate both structured proteins [84,85] and unstructured peptides [86][87][88][89][90][91]. For water, a modified TIP3P water model with its bond lengths constrained with SHAKE/RATTLE [92] was used. All simulations were performed using the NAMD2 [93] molecular modeling package using IBM Blue Gene supercomputers with a 2 fs time step in a NPT ensemble at 325 K and 1 atm. The temperature was controlled using the Langevin dynamics scheme, and the pressure was controlled using the Nosé-Hoover Langevin piston pressure control pressure coupling implemented in NAMD.
A cutoff distance of 5 Å between heavy atoms was considered to define a contact between two residues. A peptide was considered to be the component of an oligomer that is complexed with inhibitor, if it simultaneously forms more than five contacts with the inhibitor and another peptide. For the quaternary contact probability determination, all dimeric combinations of peptides, in which any one monomer forms more than five contacts with the inhibitor, were considered. The secondary structure was determined using the STRIDE program [94].
The residence times of the inhibitor-bound peptides were estimated by means of a survival time correlation function S(t), similar to what has been widely used to compute water residence time in simulations [95]. The correlation function can j remains inhibitor-bound (forms more than five heavy atom contacts with the inhibitor) from time t to to t+t ' . S(0) gives the average number of complexed peptides and S(t) gives the average number of peptides that still remain bound after a time t. t 0 was taken to be 1 ns to allow for short excursion. Averages were calculated over all configurations sampled during a single trajectory. Results obtained from different runs were further averaged. The convergence of the binding simulations was confirmed by several reversible binding events of the peptides to both ACD and lysozyme during ,200 ns of MD (see Fig. S8 in File S1). However, it should be noted that the ,200 ns timescale might not be adequate for the full exploration of the structural changes of the peptide upon oligomerization and/or complexation. Approaches such as replica exchange, similar to previously performed work [96], therefore will likely be required, which is beyond the scope of the current study.

Supporting Information
File S1. Figures S1-S8. Figure S1. Evolutions of different sized Ab species of the control system containing only 10 peptides. Data was averaged over 50 time interval. A1: Ab monomer; A2-5: small Ab oligomer (n52-5); A6-10: larger Ab oligomer (n.5). Data for all six runs are shown. Each run is represented by a different color. Figure S2. Evolutions of different sized Ab species of the system containing 10 peptides and an ACD dimer. Data was averaged over 50 time interval. X5 uncomplexed ACD; XA1: ACD-bound Ab monomer; XA2-5: ACD-bound small Ab oligomer (n52-5); XA6-10: ACD-bound larger Ab oligomer (n.5). Data for all seven runs are shown. Each run is represented by a different color. Figure S3. Evolutions of different sized Ab species of the system containing 10 peptides and human lysozyme. Data was averaged over 50 time interval. X5 uncomplexed lysozyme; XA1: lysozyme-bound Ab monomer; XA2-5: lysozyme-bound small Ab oligomer (n52-5); XA6-10: lysozyme-bound larger Ab oligomer (n.5). Data for all five runs are shown. Each run is represented by a different color. Figure S4. Evolutions of different ACD/lysozyme-complexed Ab species. 1 ns running average and snapshots at ,200 ns of aggregates in presence of ACD dimer (a) and in presence of lysozyme (b) are shown. Species An represents an Ab aggregate of size n. Figure S5. Structural changes of amyloid inhibitor proteins. (a) Evolutions of C a root-mean-square deviation (RMSD, in Å ) from the native structure of ACD domains (left and middle panels) and of lysozyme (right panel). Different colors represent different runs. (b) Time-averaged root-mean-square fluctuation (RMSF, in Å ) per residue from the native structure for the ACD domains and for lysozyme. Figure S6. Secondary structure analysis. (a) Total secondary structure population (in %) averaged over all ,200 ns runs: black -control system; red -ACD-bound; green -lysozyme-bound. The standard deviations were estimated by splitting the data into two equal sets. (b) Residue-based a-helix and b-strand population (in %) averaged over all ,200 ns runs. Some transient helix formation is notice for all three systems. ACD-bound peptides show slightly higher helix population in the C-terminal region. Figure S7. Structural changes of Ab peptides. (a) Evolutions of the C a root-mean-square deviation (RMSD, in Å ) from the initial fibril structure of the ten Ab peptides during first 10 ns of a particular control run. Each color corresponds to a different peptide. (b) The structures of the peptides (shown in ribbon representation) at 5 ns. Figure S8. Evolution of inhibitor-peptide contacts. Number of ACD-Ab contacts (a) and lysozyme-Ab contacts (b) during a typical run as a function of simulation time. Each monomer is shows using a different color. Several binding/unbinding events are observed during ,200 ns simulation. doi:10.1371/journal.pone.0113041.s001 (DOC)