Disordered Binding of Small Molecules to Aβ(12–28)*

Background: Inhibition of pathogenic protein aggregation by small molecules is poorly understood. Results: Aggregation inhibitors alter the free energy landscape of a relevant fragment of Alzheimer amyloid-β peptide in subtle but complex fashion. Conclusion: Intrinsic disorder of disease proteins persists at the level of binding small molecules. Significance: Hallmark characteristics and efficacy of inhibitors can be reconciled with lack of specificity. In recent years, an increasing number of small molecules and short peptides have been identified that interfere with aggregation and/or oligomerization of the Alzheimer β-amyloid peptide (Aβ). Many of them possess aromatic moieties, suggesting a dominant role for those in interacting with Aβ along various stages of the aggregation process. In this study, we attempt to elucidate whether interactions of such aromatic inhibitors with monomeric Aβ(12–28) point to a common mechanism of action by performing atomistic molecular dynamics simulations at equilibrium. Our results suggest that, independently of the presence of inhibitors, monomeric Aβ(12–28) populates a partially collapsed ensemble that is largely devoid of canonical secondary structure at 300 K and neutral pH. The small molecules have different affinities for Aβ(12–28) that can be partially rationalized by the balance of aromatic and charged moieties constituting the molecules. There are no predominant binding modes, although aggregation inhibitors preferentially interact with the N-terminal portion of the fragment (residues 13–20). Analysis of the free energy landscape of Aβ(12–28) reveals differences highlighted by altered populations of a looplike conformer in the presence of inhibitors. We conclude that intrinsic disorder of Aβ persists at the level of binding small molecules and that inhibitors can significantly alter properties of monomeric Aβ via multiple routes of differing specificity.

Alzheimer disease (AD) 3 is the most common form of dementia in the elderly. Strong genetic, physiological and biochemical evidence suggests that the ␤-amyloid peptide (A␤) plays a key role in the pathogenesis of AD (1). Neuropathological changes in the brain of AD patients include neuronal death in the regions related to memory and cognition as well as the abnormal presence of intra-and extracellular protein aggre-gates (2, 3) known as neurofibrillary tangles and amyloid plaques. They are the final results of a complex series of oligomerization and polymerization events that typically follow a nucleation-dependent mechanism (4). The left-hand side of Fig. 1 shows a schematic illustrating a few steps along the pathway of A␤ fibrillization. The nucleus is typically assumed to be a larger oligomer (4 -6), and the nucleation event itself may be linked to a critical structural transition involving tertiary and quaternary contacts within such an oligomer or protofibril (5). Subsequent monomer addition appears to be the dominant mode of fibril elongation (4). Peptide aggregation processes have been studied in depth with several experimental (7,8) and computational techniques (9 -12) but often remain poorly understood. Although little is known about the link between the aggregation mechanism and neurotoxicity (13), experimental evidence indicates that soluble oligomers and fibrillar precursors of A␤ may be the dominant neurotoxic species (14).
In recent years, increasing evidence points to a link between disease and disorder, specifically the functions and properties of intrinsically disordered proteins (IDPs) and polypeptide stretches within proteins (15,16). The ensembles explored by such sequences, which are estimated to make up about 20% (17) of eukaryotic genomes, are highly diverse and devoid of long lived, "folded" conformers (18). Extensive analyses have shown that simple sequence-based classifiers, such as mean hydrophobicity or net charge, can be used to distinguish folded proteins from IDPs (19). A␤40/42 belongs to the class of collapsed-disordered IDPs (20) on account of its low net charge and high hydrophobicity (21,22). IDPs often attain partial order upon functional or deleterious interactions with folded proteins or with other IDPs (23). Indeed, pathogenic self-assembly can be viewed as a specific variant of the latter case. Given that collapse and aggregation are guided by the same driving forces, it is perhaps not surprising that IDPs, such as A␤ or polyglutamine, are associated with protein aggregation diseases (24 -26).
Inherently, structural drug design aimed at finding compounds that interfere with an IDP-mediated process faces the challenge that structural targets emerge only later on the pathway. Nevertheless, the identification and detailed biophysical characterization of small molecules that modulate A␤ peptide self-assembly are expected to generate new lead candidates for clinical studies. Several therapeutic strategies have been suggested for blocking key steps in the amyloid aggregation proc-ess, including the direct inhibition of aggregation by using either peptides or small molecules (27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38). As an example, indole derivatives inhibited fibril formation of A␤ peptide (39,40) and lysozyme (41). Anthraquinones were shown to be inhibitors of Tau protein (42) and A␤40 aggregation (37), and hybrid molecules bearing both indole and quinone rings have been effective in the recovery of a fly model of AD (43). In addition, antioxidants (e.g. resveratrol (44,45) and epigallocatechin-3-gallate (46)) and non-steroidal anti-inflammatory molecules, such as naproxen (47,48), revealed new biological activities in the inhibition of amyloid aggregation. Recent x-ray microcrystallography (49,50) and solid-state nuclear magnetic resonance (NMR) spectroscopy (51) studies have provided atomistic information on the interactions between small molecule binders and amyloid fibrils. Fig. 1 illustrates why this may be less relevant than the interactions of inhibitors with soluble peptide species. In essence, compounds that specifically bind fibrils (step VI in Fig. 1) may destabilize the latter (52) but will have little impact on the association and conformational equilibria prior to nucleation (steps I and II). An alternative mechanism of inhibition could be a depletion of nucleation-competent (53) and/or toxic oligomers (54) either by stabilization of low molecular weight species, such as monomers and dimers (steps III and IV), or stabilization of larger off-pathway oligomers (step V). Given the disordered nature of the binding partner (55), it is quite reasonable to stipulate that small molecules can have differential effects for all indicated steps, including the known ability to increase the rate of fibrillization (56,57). The complexity is exacerbated by the fact that the dominant pathways may shift in a dose-dependent manner. Fig. 1 implies that studies of the binding equilibria of monomeric A␤ with inhibitors can yield insight regarding the molecular mechanisms of inhibition.
Here, we use molecular dynamics (MD) simulations to analyze 10 different small molecule inhibitors of A␤ peptide aggregation and focus on their influence on the free energy surface of monomeric A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28). The choice of studying a truncated construct is motivated by three reasons. First and foremost, it is important to be able to obtain statistically reliable simulation results. Conformational transitions in the full-length alloforms can occur on time scales that exceed the currently accessible regime (58). Second, residues 12-28 highlight the role of the so-called central hydrophobic cluster (59), residues 17-21, which is often assumed to be critical in mediating peptide-inhibitor (60) as well as peptide-peptide interactions (61). By discarding the hydrophobic C terminus, our simulations allow us to delineate the possible specific roles played by the residues in this stretch. Truncation of residues 1-11 is justified by experimental (62) and simulation (21) studies that show this segment to be completely unstructured. Third, segment 12-28 could be used in concentrations high enough to be suitable for solution NMR spectroscopy experiments (43) because it has lower olig-FIGURE 1. Schematic depicting the coupled equilibria that could be involved in inhibition of fibrillization and/or oligomerization of A␤ by small molecules. Largely unstructured peptides are shown as gray ribbons with the central hydrophobic cluster highlighted in yellow. Peptides in fibril-compatible conformations are shown in light red, and inhibitor molecules are shown in blue. Square brackets indicate conformational equilibria at different assembly levels, and curly brackets indicate a repeating unit replicated along the indicated axis. Steps I and II pertain to the unperturbed, nucleation-dependent aggregation pathway. On-and off-pathway assembly steps beyond the dimer are not shown explicitly. Steps VII and VIII are the analogous steps with inhibitor bound to the aggregating peptides. Finally, steps III-VI describe binding equilibria to various peptide species. Preferential interactions of the central hydrophobic cluster with inhibitor molecules containing aromatic moieties have been postulated (81). See "Results and Discussion" for further details. omerization and fibrillization propensities than A␤40 and A␤42. This implies that it will be easier to derive testable hypotheses. We use the cut-based free energy profile (cFEP) method (63) to identify the metastable states of monomeric A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) and the change of their relative stability upon inhibitor binding.

EXPERIMENTAL PROCEDURES
Implicit Solvent Simulations-Simulations were performed with the CHARMM program (64). The A␤(12-28) peptide and inhibitors were modeled using the united atoms CHARMM PARAM19 force field with its default truncation scheme for non-bonded interactions (cut-off of 7.5 Å). Parameters for 1,4napthoquinon-2-yl-L-tryptophan (NQTrp), anthracene, and 9,10-anthraquinone were derived as reported (37,43). Protonation states of titratable residues were considered at neutral pH. In particular, the His side chains of A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) and ␤-Ala-His were neutral (protonated at the N ␦ ), whereas the charges of the Asp/Glu and Arg/Lys side chains were Ϫ1 and ϩ1 electronic units, respectively. The net charge of the A␤(12-28) segment is zero because there are two positively charged residues (Lys-16 and Lys-28) and two negatively charged residues (Glu-22 and Asp-23), and the N and C terminus were capped with acetyl and N-methylamide groups, respectively. The electrostatic contribution to solvation was accounted for by using FACTS (65), an efficient generalized Born implicit solvent model based on the fully analytical evaluation of the volume and spatial symmetry of the solvent that is displaced from around a solute atom by its neighboring atoms. The non-polar contribution to the total effective solvation energy was approximated by a term proportional to the solvent-accessible surface area of the solute using a surface tension-like, multiplicative parameter of 7.5 cal mol Ϫ1 Å Ϫ2 . Starting conformations were prepared by placing fully extended A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) in the presence or absence of a single molecule of the inhibitor in the simulation box (1:1 concentration ratio). Simulations were carried out with periodic boundary conditions at a fixed peptide concentration of ϳ2.5 mM (87-Å cubic simulation box) using the Langevin integrator at low friction (coefficient of 0.15 ps Ϫ1 ) and at a temper-ature of 300 K. Using a time step of 2 fs, for each system, we performed three independent runs of 5 s each.
Explicit Solvent Simulations-Using GROMACS version 4.5.3 (66), capped A␤(12-28) was simulated in a cubic box of 60-Å side length in the isothermal-isobaric ensemble. The velocity rescaling thermostat of Bussi et al. (67) was used to keep a constant temperature of 310 K, whereas an ambient pressure of 1 bar was maintained using the Parrinello-Rahman barostat (68). The peptide was represented with the CHARMM27 all-atom force field, including CMAP corrections (69). The bath consisted of a solution of ϳ150 mM NaCl in TIP3P water (70). Electrostatic interactions were modeled by the particle mesh Ewald method (71). All real space interactions were truncated at 12 Å. Neighbor lists were recalculated every five steps. LINCS (72) was used to constrain all bonds involving hydrogen atoms to their parameter-derived values. The time step was 2 fs, and we obtained three independent simulations starting from random, extended structures that each are 380 ns in length, the first 20 ns of which we discarded as equilibration. Preliminary analyses of secondary structure propensities or contact patterns revealed that, given the reduced amount of sampling and increased friction, statistical convergence for the majority of readouts could not be obtained. Therefore, data from explicit solvent simulations are only included in Fig. 2.
cFEP Analysis-The 750,000 snapshots of each system were clustered by the Leader algorithm as implemented in Wordom (73) using the distance root mean square deviation of C ␣ atoms of residues 14 -24 and a threshold of 1.0 Å. The cFEP (63) technique was used to identify metastable states of monomeric A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) and the change of their relative stability upon inhibitor binding. The input for the cFEP calculation is the network of conformational transitions, which is derived from the direct transitions between clusterized snapshots (nodes of the network) sampled at a given time interval (20 ps here) along the MD simulations. For each node, nodes are partitioned into two groups using the values of the mean first passage times to the reference node to define a cut. The free energy is related to the maximum flow across the cut and approximated as ⌬G ϭ ϪkTln(Z AB ), where Z AB is the partition function of the mean first passage time-based cutting surface (for further details, see Ref. 63). The result is a one-dimensional profile along a reaction coordinate (the relative partition function, termed Z A /Z) that preserves the barrier height between well-separated free energy basins.
Monomeric A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) Is Partially Collapsed and Disordered-Visual inspection of the trajectories showed that A␤(12-28) does not attain any specific, long lived structure akin to a folded ensemble. Conformational transitions are rapid and yield a disordered ensemble. To quantitatively assess the overall polymeric state of the A␤ peptide, we computed the scaling of internal distances with sequence spacing as well as the angular correlation function, as described in previous work (74). The data in Fig. 2 indicate that, independently of the presence of an inhibitor, the peptide populates a partially collapsed ensemble. Inhibitors appear to be able to cause both compaction and swelling of A␤(12-28), but many of the differences are insignif-icant. For fully globular species, one would expect the internal scaling plot to yield a plateau (75) similar to what we observed for the full-length alloforms (21), whereas the theoretical prediction for a chain in a good solvent is significantly more expanded. As described under "Experimental Procedures," we performed calculations in explicit solvent of the free system. These data are shown as well in Fig. 2. They crudely illustrate similarity between implicit and explicit solvent ensembles ( Fig.  2A) and simultaneously demonstrate the difficulty to obtain converged explicit solvent results even for low dimensional readouts, such as the angular correlation function (Fig. 2B).

Disordered Binding of Small Molecules to A␤(12-28)
DECEMBER 2, 2011 • VOLUME 286 • NUMBER 48 tors bind to, Fig. 4 shows intra-and intermolecular contact maps for the free system as well as for simulations in the presence of inhibitors. The most frequently observed intermolecular contacts are shared by all inhibitors and involve mainly the N-terminal segment (residues [13][14][15][16][17][18][19][20]. With the exception of ␤-Ala-His, which largely remains dissociated, the large hydrophobic side chains of Phe-19 and Phe-20 constitute the site of highest interaction probability in all cases. It is interesting to note that the larger peptidic inhibitors appear to show more specific contact patterns than, for example, anthracene or 9,10anthraquinone. This is consistent with the complexity of the interfaces presented by each molecule; anthracene is a completely homogeneous tricyclic molecule, whereas the tetrapeptides have three different aromatic moieties (two of which have polar sites), one or two formal charges, and a mainly rigid spacer. The segment 24 -28 appears to be largely inert to inhibitor binding, consistent with the fact that residues in this region do not feature prominently in sequence analyses (62,78,79), mutation (80), or fragment binding studies (61) as being responsible for amyloid formation. Although this is also true for the N-terminal residues we truncated, the same cannot be said for C-terminal residues 29 -40/42. A priori, we have no reason to assume that inhibitors would not bind to this portion of A␤ (see Fig. 1). However, the questions in this work center around the interaction of aromatic inhibitors with the central hydrophobic core as the suspected site of highest affinity (81). Given that several of the inhibitors have significant impact on oligomerization and fibrillization (36,43) even at subequimolar concentration ratios, this may represent a reasonable simplification.
We can attempt to explain the interaction patterns within the confines of the employed computational model by decomposing system energetics. As an example, we focus on NQTrp, which has the highest affinity for A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) in the MD simulations (see Table 1) and is also one of the most potent inhibitors of A␤ peptide aggregation in experiments (43). In Fig. 5, the decomposition of the dominant term of the intermolecular energy into contributions from individual pairs of functional groups shows that the two aromatic moieties of NQTrp make favorable van der Waals interactions with the entire N-terminal stretch of the peptide (residues [13][14][15][16][17][18][19][20]. In addition, binding appears to feature favorable electrostatic interactions involving the (charged) carboxyl group of NQTrp and peptide residues 12-16, which possess a wealth of polar hydrogens (His-13, His-14, Gln-15, and Lys-16). This can be inferred indirectly from the favorable van der Waals interactions between the carboxyl group and the peptide. We did not consider electrostatic interactions here because of effective multibody terms preventing pairwise decomposition. In general, good correspondence is seen between the interaction energy matrix and contact maps indicating that binding is largely enthalpic. This is expected in particular given that entropic contributions to ligand binding stemming from the solvent are accounted for implicitly in the continuum model.
It is possible to rationalize the relative affinities for A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) to the 10 inhibitors by focusing on the three main contributions (i.e. unfavorable desolvation of hydrophilic moieties, favorable burial of hydrophobic moieties, and favorable van der Waals interactions) (see Table 1 and supplemental Table S2). The total polar desolvation penalty ranges from 1 to 5 kcal/mol and scales roughly with the size of the inhibitor. No persistent salt bridges are formed, and the contribution is generally unfavorable. Burial of hydrophobic surface contributes favorably. This term correlates with the number of aromatic moieties present on the inhibitor. Last, dispersive interactions between inhibitor and A␤(12-28) contribute the bulk of the favorable effective binding energy. It appears as if this contribution becomes less predictable with increasing numbers of hydrophobic moieties present on the inhibitor (e.g. NQTrp has a significantly more favorable van der Waals contribution than either Tyr-Aib-Trp-Phe or Tyr-Pro-Trp-Phe despite possessing fewer aromatic moieties). The computed effective binding energies appear to correlate by rank order with the fractions bound (F b in Table 1) reasonably well. Two exceptions are as follows. The first is Tyr-Pro-Phe-Phe, which appears to incur a significant entropic penalty upon binding that is consistent with a significantly more structured free energy surface of A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) in the presence of Tyr-Pro-Phe-Phe (see supplemental Fig. S7). On the contrary, anthracene exhibits high affin-

TABLE 1 Small molecule inhibitors and their affinity to A␤(12-28)
a Aib, ␣-aminoisobutyric acid; NQTrp, 1,4-napthoquinon-2-yl-L-tryptophan; Tyr-Aib-Trp-Phe, designed derivative of endomorphin-1; Tyr-Pro-Trp-Phe, endomorphin-1 with charged carboxyl group at the C terminus; Tyr-Pro-Phe-Phe, endomorphin-2 with charged carboxyl group at the C terminus; Tyr-Pro-Trp-Phe-NH 2 , endomorphin-1; Tyr-Pro-Phe-Phe-NH 2 , endomorphin-2; ␤-Ala-His, carnosine. Note that the endogenous endomorphins have the -NH 2 group at the C terminus. b F b is the fraction of snapshots in which any atom of the inhibitor is within 7.5 Å of any atom of A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28). Values are given as percentages. c Each of the these three terms (van der Waals terms (vdW), electrostatic interactions (El), and nonpolar solvation terms (Np)) was calculated by subtracting the energy of A␤(12-28) and inhibitor in the isolated state from the energy in the ensemble of bound conformations. d The effective binding energy is the sum of the changes in the van der Waals energy, electrostatic energy, and non-polar solvation energy upon binding. All values are reported in kcal/mol. They include all contributions to the binding free energy except for changes in entropies of the solutes. ity despite its modest effective binding energy. Here, the entropic penalty at the inhibitor level is essentially zero (rigid molecule), and the contact map indicates the most degenerate binding (see Fig. 4), suggesting a minimal entropic penalty at the peptide level as well. Returning to Fig. 4, we note that inhibitor binding has an impact on intramolecular contacts of A␤(12-28) as well. Although the contact maps continue to indicate degenerate long range interactions within the peptide, the presence of inhibitors seems to enhance contacts between residues 12-15 and 21-26 (marked in the plots). This is a relatively weak effect that is observed for all inhibitors but ␤-Ala-His and most prominently for NQTrp. It points to the ability of molecules composed of similar building blocks to exert a generic effect on the conformational properties of A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28), and this is discussed next.
As noted above, the presence of inhibitors does seem to enhance intramolecular A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) contacts between residues 12-15 and 21-26 (see Fig. 4). This points to the potential of inhibitors to alter the free energy surface of A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) in a manner that cannot be captured clearly by evaluating ensemble-averaged readouts like secondary structure propensities. Cut-based FEPs represent an appropriate way to condense trajectory information and to show approximately the distributions of barriers and basins. In Fig. 3, free A␤(12-28) exhibited no predominantly populated conformation. When clustering  data using the C ␣ atoms of residues 14 -24, the most populated conformer corresponds to a straight helical structure (see Fig.  7) with a disordered C terminus. The entire helical basin encompasses partially helical as well as completely helical structures that constitute a total statistical weight of about 10%. It is separated by a wide barrier region composed of minor basins with partially helical states (population of about 10%) from a broad entropic basin (70%). The latter consists of fluctuating conformers devoid of regular secondary structure content. Supplemental Figs. S2-S11 show the same type of data for simulations in the presence of inhibitors. In all cases, a large entropic basin has the largest statistical weight, indicating that inhibitors are not able to lock A␤(12-28) into a specific conformation. There are changes, however, to the relative weights of ordered conformers. In particular, a basin is increasingly populated that corresponds to a compact structure characterized by a specific loop conformation spanning residues 14 -24. It is stabilized (see Fig. 7) by the formation of a hydrogen-bonded network of side chains including Asp-23, His-13, and either Gln-15 or His-14. Its statistical weight for each inhibitor is summarized in supplemental Table S1 and ranges from ϳ2 to 20%. Given that the population of the loop is lowest for the free system and in the presence of largely inert ␤-Ala-His and that it is only transiently populated in either case (see supplemental Figs. S12 and S13), one may ask how a specific A␤(12-28) conformation can be universally enhanced by other inhibitors in the absence of a specific binding mode. The answer is that the inhibitors provide an additional nonaqueous interface (i.e. they allow patterns of sequestering residues from solvent to change). Normalized by their propensity to bind A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28), the indole-containing inhibitors NQTrp (see supplemental Table S1) and D Trp-Aib exert the largest effect in this regard. Indole groups have been heavily implicated in A␤ aggregation inhibitor design (39) and were also analyzed in systematic fashion as inhibitors of hen egg white lysozyme aggregation (41). Interestingly, the inhibitor is not required to interact directly with the polar residues mentioned but can act indirectly or allosterically. Such a mechanism of action is entropically favored on account of the peptide's high intrinsic flexibility (this is true, for example, for D Trp-Aib, as seen in supplemental Fig. S14). However, supplemental Fig. S14 also shows the following counterexample. Direct binding of anthracene to the side chains of Asp-23 and Gln-15 occurs with greater frequency than binding in general, and population of the loop conformer in the absence of binding is essentially identical to that seen for the free system. These data resemble a conformational selection mechanism described in binding equilibria of intrinsically disordered proteins (82).
An interfacial effect as described is intriguing because it allows for an explanation as to why so many different inhibitors, which share some structural hallmarks, have been characterized (83,84). If one compares the requirements for small molecule design in enzyme inhibition with that of inhibition of oligomerization and fibrillization, one would be forced to conclude that the intrinsic disorder of the target translates to the inhibitor level. This could imply that "polyfunctional" moieties combining largely hydrophobic parts with polar sites are well suited to bind disordered A␤. Disordered interactions of such poly-functional units with peptide moieties may also explain why mutation studies have failed to establish the necessity for aromatic residues Phe-19 and Phe-20 in A␤ to be present for aromatic inhibitors of the general flavor tested here to be effective (85).
It should be noted that the partial desolvation of a charged moiety (Asp-23) may raise questions about the accuracy of the computational model in use. We wish to emphasize that we assign little importance to the structural details of the aforementioned loop structure on account of these concerns, although desolvation of Asp-23 is seen experimentally in the NMR structures (86) and in explicit solvent simulations (87) of similar fragments. It is worthwhile to point out that in our simulations, the statistical weight of the loop never exceeds 20%, meaning that most computed ensemble averages would only be moderately affected.

CONCLUSIONS
The FACTS implicit solvation model allowed us to obtain data with statistical errors that permit establishing subtle, quantitative effects of inhibitor binding (e.g. see Fig. 6). Therefore, five main results emerge from the comparative analysis of MD simulations of A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) alone and in the presence of small molecules that have been shown experimentally to interfere with A␤ peptide self-assembly. 1) The free energy surface of A␤(12-28) shows a broad entropic basin devoid of a predominant conformation ( Fig. 3 and supplemental Figs. S1-S11). Upon inhibitor binding, significant but subtle changes to the free energy landscape occur, as exemplified by changes in average secondary structure propensities and intramolecular contacts (Figs. 4 and 6). 2) Different inhibitors share common intermolecular interactions, but none of them exhibits a specific binding mode irrespective of binding affinity (Table 1 and Fig.  4). 3) Differences in affinity can be partially rationalized by the relative number of aromatic groups and charged groups in the inhibitors ( Table 1). The former provide a favorable contribution through hydrophobic interactions mainly with Phe-19 and Phe-20 and through mixed polar and nonpolar interactions with residues 13-18. The desolvation of charged groups is generally unfavorable (i.e. inhibitor binding does not rely on salt bridge formation) (Figs. 4 and 5). 4) The simulation data demonstrate that detailed predictions of interactions at the molecular level cannot just rely on simple heuristics (92). As an example, the relative binding properties of the different endomorphin variants appear nearly impossible to rationalize with purely sequence-based approaches (Table 1). 5) The data show how small molecules composed of similar building blocks can incur a generic interfacial effect. Such effect is the cause of the enhancement of a specific loop conformation of A␤(12-28) (supplemental Table S1 and Fig. S13).
Taken together, the results show how aggregation inhibitors can have subtle but significant effects on the behavior of a fragment of A␤ encompassing the central hydrophobic cluster that is most commonly implied in the peptide's amyloidogenicity. It is important to ask whether our results could apply to other aggregation-prone IDPs as well. We use ␣-synuclein, the disease protein of Parkinson disease, as an example, which is significantly larger than A␤ and adopts more extended conformations in solution (93). Despite large differences in sequence properties, monomeric ensembles, and oligomer distributions, there exists a comparable range of compounds possessing one or more aromatic moieties that have been shown to bind monomeric ␣-synuclein (94) and to interfere with ␣-synuclein aggregation (53,(95)(96)(97)(98) and oligomerization (99,100). It is not necessary and perhaps unlikely that all of these inhibitors act in equivalent fashion for diverse systems. Returning to Fig. 1, this means, for example, that the multiple equilibria involving inhibitor binding may not all contribute significantly. As an example, our data for ␤-Ala-His suggest that this compound is unlikely to interfere with A␤ dimerization at the low concentrations typically in use in vitro. Similarly, D Trp-Aib exhibited no significant effects on early oligomer formation of A␤  at concentration ratios of up to 40:1 excess of D Trp-Aib (40) and is also largely unbound in our simulations. This suggests a specific role in step VI for those two compounds. Conversely, evidence for generic effects at the oligomer level (in particular step V in Fig. 1) is not only given in the wider context of enzyme activity assays (101) but has also been proposed specifically in the context of aggregation experiments (102).
Finally, the consistency between simulation results and experimental data (NMR spectroscopy analysis of A␤ (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) and characterization of inhibition of A␤40 aggregation) suggest that several of the conclusions are independent of the details of the simulation model. Encouraged by these results, we are currently using the same methodology to perform a medium throughput screening of a novel class of compounds meant to interfere with A␤ oligomerization and fibrillization.