Sterol-activated amyloid beta fibril formation

The metabolic processes that link Alzheimer’s disease (AD) to elevated cholesterol levels in the brain are not fully defined. Amyloid beta (Aβ) plaque accumulation is believed to begin decades prior to symptoms and to contribute significantly to the disease. Cholesterol and its metabolites accelerate plaque formation through as-yet-undefined mechanisms. Here, the mechanism of cholesterol (CH) and cholesterol 3-sulfate (CS) induced acceleration of Aβ42 fibril formation is examined in quantitative ligand binding, Aβ42 fibril polymerization, and molecular dynamics studies. Equilibrium and pre-steady-state binding studies reveal that monomeric Aβ42•ligand complexes form and dissociate rapidly relative to oligomerization, that the ligand/peptide stoichiometry is 1-to-1, and that the peptide is likely saturated in vivo. Analysis of Aβ42 polymerization progress curves demonstrates that ligands accelerate polymer synthesis by catalyzing the conversion of peptide monomers into dimers that nucleate the polymerization reaction. Nucleation is accelerated ∼49-fold by CH, and ∼13,000-fold by CS — a minor CH metabolite. Polymerization kinetic models predict that at presumed disease-relevant CS and CH concentrations, approximately half of the polymerization nuclei will contain CS, small oligomers of neurotoxic dimensions (∼12-mers) will contain substantial CS, and fibril-formation lag times will decrease 13-fold relative to unliganded Aβ42. Molecular dynamics models, which quantitatively predict all experimental findings, indicate that the acceleration mechanism is rooted in ligand-induced stabilization of the peptide in non-helical conformations that readily form polymerization nuclei.

The metabolic processes that link Alzheimer's disease (AD) to elevated cholesterol levels in the brain are not fully defined.Amyloid beta (Aβ) plaque accumulation is believed to begin decades prior to symptoms and to contribute significantly to the disease.Cholesterol and its metabolites accelerate plaque formation through as-yet-undefined mechanisms.Here, the mechanism of cholesterol (CH) and cholesterol 3-sulfate (CS) induced acceleration of Aβ 42 fibril formation is examined in quantitative ligand binding, Aβ 42 fibril polymerization, and molecular dynamics studies.Equilibrium and pre-steady-state binding studies reveal that monomeric Aβ 42 ligand complexes form and dissociate rapidly relative to oligomerization, that the ligand/peptide stoichiometry is 1-to-1, and that the peptide is likely saturated in vivo.Analysis of Aβ 42 polymerization progress curves demonstrates that ligands accelerate polymer synthesis by catalyzing the conversion of peptide monomers into dimers that nucleate the polymerization reaction.Nucleation is accelerated 49-fold by CH, and 13,000fold by CSa minor CH metabolite.Polymerization kinetic models predict that at presumed disease-relevant CS and CH concentrations, approximately half of the polymerization nuclei will contain CS, small oligomers of neurotoxic dimensions (12-mers) will contain substantial CS, and fibrilformation lag times will decrease 13-fold relative to unliganded Aβ 42 .Molecular dynamics models, which quantitatively predict all experimental findings, indicate that the acceleration mechanism is rooted in ligand-induced stabilization of the peptide in non-helical conformations that readily form polymerization nuclei.
Clinical studies estimate that 12% of United States citizens aged 65 and older suffer from Alzheimer's dementia (1) and 34% of those over age 85 have the disease.Collateral consequences of the disease include approximately 15 billion hours of annual caregiving by family and non-family members-a considerable societal stress.The fiscal burden of Alzheimer's disease (AD) in 2022 is estimated at 0.6 trillion dollars in the United States and in the absence of mitigating factors is expected to rise as the majority of the baby-boom generation enters the over-65 age category.
Roughly 15 years (2,3) prior to the onset of symptoms, AD is thought to begin with the dysregulation of metabolic processes that include elevated production of Aβ peptides-a quintet of overlapping peptides (36-42-mers) proteolytically clipped by βand γ-secretase from a trans-membrane segment of the amyloid precursor protein (APP) (4).Aβ peptides are amyloidogenicthey self-organize into dimers (polymerization nuclei) that rapidly add monomers to form oligomers, proto-fibrils, fibrils, and ultimately dense nests of fibrils known as senile plaques.The preponderance of evidence over the last several decades (5-7) supports that certain, as yet undefined small soluble Aβ oligomers, 2-to 12-mers (8) are the primary neurotoxic forms of the peptide.Cytotoxic small oligos bind synaptic receptors at sub-nanomolar affinities (9) and in so doing disrupt the intra-neuronal circuitry that underlies memory (8,10) and foster tau fibril formation (11).
CH (26,27) and CS (28) dramatically accelerate Aβ-fibril formation, yet the acceleration mechanism remains largely undefined (28).Here, in a medley of experimentation and modeling, we quantitate the interactions of the ligands (CH and CS) with the Aβ 42 peptide, define their effects on Aβ 42fibril formation, and construct molecular models that accurately describe the solution behavior of these systems and suggest a role for CS in senile plaque formation.

Sterol binding to Aβ 42
Equilibrium-binding studies CH (27) and CS (28) increase the rate of Aβ aggregation and CH is thought to stabilize fibrils (29); yet, the affinities of CH and its metabolites for the Aβ peptide monomer have not been determined.Here, CH and CS affinities for the Aβ 42 monomer are established using dehydroergosterol (DHE)-a fluorescent CH analog (30) used as a competitive probe to determine CH and CS affinities.Aβ 42 monomers were prepared as previously described (31)     Similar to other titrations involving CH (35)(36)(37), the CH and CS competition titrations (Fig. 1, C and D) are wellbehaved and consistent with monomeric ligand.CH was reported in 1973 to form micelles with a 25 to 40 nM critical micelle concentration (CMC) (38); however, subsequent studies could not detect micelles at a concentration as high as 4.0 μM (39-41) and call into question the solution behavior of CH and its metabolites (41).The Figure 1, C and D insets highlight the titration regions that span the published CH and CS (28,38) CMCs, which are indicated by vertical arrows.As evidenced by the excellent fits of the single-site binding model, the titrations predict the same K d above and below the CMC; thus, CH and CS show no signs of aggregation throughout the titrations.
Aβ 42 spontaneously forms fibrils, albeit slowly, in the absence of ligands, and polymerization is accelerated by CH and CS.It is thus important to establish that the ligand binding studies were performed on timescales short enough to avoid complications due to polymer formation.To do so, polymerization time-course controls (see Fig. S1) were run at the highest ligand and Aβ 42 concentrations (i.e., maximum oligomerization rates) associated with the Figure 1 titration.Polymerization was monitored using ThT, a fluorescent ligand  1.
The Aβ 42 oligomerization mechanism widely used to detect Aβ 42 oligomers ≥5-mers (42,43).In the <30 min required to complete the Figure 1, A and B titrations, the control progress curves (Fig. S1, A and B 1. The monophasic nature of the DHEbinding reactions is consistent with binding to a single form of Aβ 42 and the coincidence of k off /k on (17 ± 2 nM) and K d (16 ± 1 nM) suggests that equilibrium and pre-steady state measurements monitor interactions among the same species.The on-rate constants for formation of all three complexes range from 2 to 6 × 10 7 M −1 s −1 and are close to the value calculated for the diffusion encounter of DHE and Aβ 42 , 9.3 × 10 7 M −1 s −1 , using the DHE diffusion constants and Stokes radii (46,47) and Aβ 42 (48,49); hence, components of the complexes exchange rapidly and, as will become apparent, complex formation and dissociation does not contribute meaningfully to the rate of Aβ 42 -oligomer formation.

CH and CS accelerate Aβ 42 nucleation
The effects of CS and CH on Aβ 42 oligomerization were assessed by monitoring fibril formation in the presence and absence of ligands using ThTa fluorescent sensor that binds Aβ oligos ≥5-mers (42,43) and does not perturb polymerization progress curves at concentrations below 50 μM (50).Reactions were initiated by the addition of ligand (at saturation) or buffer (control) to a fresh solution of Aβ 42 and ThT (see Fig. 3 Legend).Reactions were performed in triplicate and the averaged data are presented in Figure 3.Such progress curves are often fit using a generalized sigmoidal  function and compared on the basis of lag-time length and elongation-phase slope.Here, progress curves are fit numerically to the Nucleation-Elongation-Fragmentation (NEF) model (51,52), using Copasi (53).Numerical modeling allows one to assess whether a particular mechanism adequately predicts experimental behavior and provides rate constants for the steps of the mechanism that can be compared across peptideligand combinations to identify where and to what extent ligands induce change.
The NEF model assumes a slow, energetically unfavorable event generates a polymerization nucleus that rapidly adds monomers (at the elongation rate) to form oligomers.The reaction accelerates in a geometric fashion as oligomer fragmentation produces new nuclei.The tenets of the model are embodied in Equations 1-3, which form the basis of the Copasi model (53).
where m is monomer concentration, n is the concentration of surfaces capable of adding monomer, and o is the concentration of peptides that are in the interior of the polymer and thus cannot add monomers.k nuc , k el , and k frag are the nucleation, elongation, and fragmentation rate constants.Reaction 1 of the NEF scheme assumes nucleation is second order in Aβ 42 monomer concentration.The reaction order was determined for ligand-bound and free forms of Aβ 42 by plotting nucleation rates versus [Aβ 42 ] n , where n, the reaction order, is 1, 2, or 3-such plots become linear only when n equals the reaction order (54).Nucleus formation was monitored via ThT fluorescence in the region of the progress curve where nucleation is rate limiting-the very early stage of the lag phase.Rates were obtained by linear least-squares fitting of progress curves.In all cases, fits were initiated at t 0 and deviation from linearity was within experimental error (i.e., χ 2 > 0.95).As is evident in Figure 4, A-C, the Rate-versus-[Aβ 42 ] n plots for all three peptide forms are linearized at n = 2; hence, the nucleation reactions are second order.The nucleation rate constants are given by the slopes of the plots (obtained by linear least-squares fitting) and are within the error of those predicted by NEF fitting, see Table 2.
The polymerization progress curves seen in Figure 3 indicate similar acceleration and elongation phases for all three curves (Aβ 42 , Aβ 42 CH and Aβ 42 CS).The NEF fits are shown as solid lines passing through the data and the associated rate constants are listed in Table 2.The NEF model predicts forward and reverse elongation rate constants that are within 1.3-and 1.4-fold of one another, respectively, and that fragmentation rate constants differ less than 1.6-fold.In contrast, the forward nucleation rate constants differ dramatically.Relative to the unliganded peptide, the nucleation rate constant is increased 49-fold by CH, and, remarkably, 13,000-fold by CSa profound acceleration of the rate at which the nuclei that polymerize fibril synthesis are produced.

Molecular dynamics analysis
To establish molecular mechanisms capable of predicting Aβ 42 behavior in the presence and absence of ligands, molecular dynamics models were developed using GROMACS (55,56).The accuracy of the models was vetted by comparing their predictions with experimental outcomes.CHpeptide-CH and Aβ 42 were allowed to freely associate over 1.0 μs.Cluster analysis, which groups structures according to their RMSD similarity (<5 Å cutoff), identified the six CHAβ 42 forms seen in Fig. S2.The predominant form, Form 1 (Fig. 5A), is present during 74% of the simulation; the remaining forms and their percent presence are as follows: 2 (8.7%), 3 (6.8%), 4 (5.2%), 5 (3.3%), 6 (1.7%).Notably, only Form 3 is devoid of α-helical structure and, as described below, is the only complex predicted to form dimers.The K d predicted for the CHAβ 42 complex, 160 nM, agrees well with the experimentally determined value of 120 ± 12 nM (see Table 2).
CSpeptide-The predicted structure of the CS complex, Figure 5B, is distinct from the CH-bound speciesthe  2.
The Aβ 42 oligomerization mechanism peptide is devoid of α-helix and encircles the central aspect of the CS carbon skeleton in a hydrophobic ring (rendered in brown).The CS sulfate moiety, which extends beyond the ring, forms a salt bridge with the K28 primary amine.Cluster analysis indicates that the ring is present during >98% of the simulation and the peptide N-terminus behaves as a random coil.The predicted CSpeptide dissociation constant, 31 nM, is in excellent agreement with the experimentally determined value, 36 ± 3 nM (see Table 2).

Aβ 42 dimers (polymerization nuclei)
Each of the eight peptide forms-six CH, one CS, and the unliganded form-was tested for its tendency to dimerize by randomly positioning two copies of a given species inside an aqueous cube and monitoring dimer formation versus time over 5.0 μs (2 ps step-size).CH monomers were constrained to remain within their clusters by a weak restoring force (56) until significant inter-peptide contact was established at which point the constraint was removed and monomers could reconfigure freely.Significant contact is defined as an interaction energy exceeding 10% of the energy required to separate two fully associated peptides (25 kJ/mole (64)).In Figure 6, A and B, the dimerization reactions are grouped according to those that either did or did not produce dimers, respectively.The grouping reveals that only monomers devoid of α-helical structure form dimers-the Form 3 CH, CS, and unliganded species.The time average of all structures in the dimerization plateaus is shown in Figure 6, C-E.The structures are highly similar, 79% β-sheet, and fully consistent with the S-shaped peptide structure seen in fibrils (65).
Unliganded Aβ 42 forms the S-shaped dimer found in fibrils slowly relative to the liganded peptide (Fig. 6A).Structural "snapshots" along the reaction coordinate reveal that unliganded Aβ 42 rapidly (3 ns) forms a single stable intermediate -a dimer containing three parallel β-sheets (Fig. 6F) that slowly transitions to the more stable S-shaped β-sheet structure seen in fibrils.The half-life for transitioning the intermediate to the S-shaped dimer, 6.0 μs, is 11,300-fold greater   a Obtained from NEF fitting fibril formation progress curves (Fig. 3).
c Parentheses enclose one standard-deviation unit.The Aβ 42 oligomerization mechanism than that for converting CS monomers to dimers, 0.53 ns-a value that compares favorably with the 13,000-fold value determined experimentally (see Table 2).Thus, the model predicts that CH and CS accelerate dimerization relative to the unliganded species by "guiding" the peptide folding reaction away from the intermediate.
To test the MD prediction that only ligand-bound monomers devoid of α-helix readily form dimers, theoretical and experimental dimerization rates were compared.Modelling indicates 100% of CS and 6.8% of Form 3 CH monomers are dimerization competent.Dimerization is proportional to the square of the monomer concentration; thus, the predicted CS/CH dimerization rate ratio is (1.0/ 0.068) 2 = 216.The experimental ratio, calculated using nucleation rate constants (see Table 2) is 261-fold.The close agreement of these values lends credence to the model and its underlying mechanism.It is notable that CS and Form 3 CH monomers form homo-and heterodimers at indistinguishable rates (see Fig. S3).

The Aβ 42 oligomer
A time course for CSAβ 42 octamer formation is presented in Figure 7A, which plots the oligomerization status of two CSpeptides versus time.The first peptide, associated with the black line (BL), forms a dimer at 6 ns; the second, associated with the red-line (RL), forms a dimer 2 ns later.The BL dimer forms a trimer and then tetramer before combining with the RL-associated trimer, which formed in the interim, to produce a 7-mer that then adds the final monomer to produce the octamer.The formation of new peptide interfaces, which appear as vertical lines, is extremely fast relative to the peptideencounter time intervals, which lengthen as the concentration of interacting species decreases.Progress curves for the interface-forming reactions, seen in Figure 7B, cluster into two groups-those that form dimers and those that add to an existing oligomer, which unlike the monomer presents a preformed β-sheet structure to the incoming species.The k obs values associated with dimer-and oligomer-interface formation are 0.76 ± 0.01 ns −1 and 2.2 ± 0.03 ns −1 , respectively; The Aβ 42 oligomerization mechanism hence, the preformed β-sheet scaffold accelerates interface formation 2.9-fold.The structure of the self-assembled octamer, depicted in Figure 6C, is fully consistent with the cryo-EM structure (66).

Oligomer fragmentation
Fragmentation, a cardinal feature of the NEF model, transitions fibril formation from the nucleus-forming, or lag phase, to the extension phase by the geometric expansion of the number of oligos undergoing polymerization (51)(52)(53).The molecular dynamics model was tested for its ability to fragment oligomers by placing CSoligomers (8-mer, 16-mer or 25-mer) in 10 × 10 × 10 nm cube containing water, PO 4 (50 mM), KCl (0.10 M), pH 7.4, 298 K, and monitoring oligomer size over a 0.10 μs time interval.While neither the 8-nor 16-mer fragmented, the 25-mer was cleaved in a nearly simultaneous double-fragmentation event into three oligos, a 7-eight-and 10-mer (see Fig. S4).

Biological inferences
Given that the nucleation rate constant is 260-fold greater for CSAβ 42 than CHAβ 42 , it is of interest to consider whether CS might meaningfully contribute to nuclei synthesis in vivo.The levels of CS in adult human brain have not been published; however, CH (67) and CS (68) levels in normal rat brain predict CS/CH ratios that range from 0.05 to 2.5% (67,68).The CH level in human cerebrospinal fluid (6.5 μM) (69) is quite high relative to its Aβ 42 affinity (120 nM) and suggests CH is saturating in vivoa perspective supported by the fact that plaques isolated from human brain are saturated in with sterols (primarily CH) in a 1-to-1 stoichiometry (15).Assuming CH and CS are saturating, and setting CS at 1% of CH on a molar basis, 3.4% of Aβ 42 is expected to reside in the CSAβ 42 complex due to the 3.4-fold enhanced affinity of CS over CH for Aβ 42 .The nucleation rate constants in Table 2 predict that at 3.4% CSAβ 42 , CS homodimer nuclei will form at one-third the rate of CH homodimers.Given that 100% of CS and 6.8% of CH monomers are dimerization competent, and that the rate constants for homo-and heterodimer formation are identical (Fig. S3), the CS/CH heterodimers will form at 64% the rate of CH homodimers.Together these values predict that 49% of polymerization nuclei will contain one or more CS.
The role of CS in small Aβ-oligo toxicity has not been considered.Neurotoxic Aβ oligos are 12 monomers in length (8).Nuclei lengthen via the addition of CH and CS monomers in their solution ratio; hence, the CS composition of a given length oligo can be calculated.Again assuming CS is 1% of CH on a molar basis, one calculates that in addition to the CS composition of the nucleus, 30% of 12-mers will contain one or more additional CS and 8% will contain two or morefor example, 30% of 12-mers initiated with CS homodimers will contain three or more CS, and 8% will contain four or more.
To experimentally assess the potential impact of CS on fibril formation in vivo, fibril synthesis was monitored over a series of CS/CH ratios that span the physiological range.As is apparent in Figure 8, at 0.1% CSthe level in human blood (70)the lag-time shortens by several hours; at 1%the level in rat brain tissue (67,68) the lag-time is nearly halved; and at 10%the level in human skin (71)the lag-time approaches that of pure CS.
The extent to which CS-accelerated nucleation contributes to the rate of plaque formation in the AD-diseased brain is not known.Should its role be significant in vivo, it is most likely to contribute in the earliest stages of the disease, perhaps prior to plaque detection, where the contribution from fibril fragmentation is at a minimum.

Conclusions
The rate constants and equilibria governing Aβ 42 monomer interactions with CH and CS were determined and reveal that Aβ 42 ligand complexes form and dissociate rapidly relative to Aβ-fibril formation.Ligand induced stimulation of fibril formation is shown to occur nearly exclusively in the nucleation phase of the reaction.Relative to the unliganded peptide, nucleation is accelerated 49-fold by CH, and, remarkably, 13,000-fold by CS.

The Aβ 42 oligomerization mechanism
Molecular dynamics models that accurately predict peptide/ ligand affinities and rate accelerations offer atomic/molecular descriptions of the fibril formation mechanism.Modeling predicts that the experimentally observed 260-fold difference in CH-and CS-induced nucleation rates are due to liganddependent differences in the dimerization competency of the monomers -100% versus 6.8% for CS-and CH-bound species and that competency is determined by the extent to which the ligand-bound species are devoid of α-helix.Relative to the unliganded peptide, CH and CS accelerate dimerization primarily by guiding the peptide folding trajectory away from a non-productive β-sheet-rich intermediate that profoundly slows its transition to a polymerization-competent dimer.Finally, experiments and modeling over presumed physiological CS/CH ranges imply that CS -might well contribute to senile plaque accumulation in the AD patient brain.

Preparation of Aβ 42 monomers
Aβ 42 monomers were prepared using a well-established method (31).Briefly, peptide is resuspended in HIFP, vortexed 30 s to form stable α-helical monomers (57), and aliquoted (50 μg/tube) into 0.5 ml Eppendorf tubes.HIFP is then evaporated (ambient temperature) in a fume hood overnight and the remaining HIFP is removed under vacuum (1 h) without heating using a SpeedVac.Samples tubes are then sealed with paraffin and stored at −20 C. Immediately prior to use, the peptide-containing tubes are warmed to room temperature and DMSO is added to create a 5.0 mM peptide stock solution that is added as needed to experimental buffers.The excess peptide is discarded after 8 h.4) (32,33,45).(28,38).Measurements were made within 5 min post-mixing to ensure <2% of Aβ 42 oligomerized during the measurements.As described previously (74), data were fit to the following competitive single-site-binding model equation (Equation 5):

Sterol binding to
The Aβ 42 oligomerization mechanism  immediately prior to use.The nucleation rate for each condition was obtained by a linear least-squares fitting of the very early region of the fibril formation lag phase.All fits were initiated at t 0 and deviation from linearity was within experimental error (i.e., χ 2 > 0.95).Measurements were performed in triplicate and plotted versus [LigandAβ 42 ] 2 .Rate constants were obtained by linear least-squares fitting of the Rate-versus-[LAβ 42 ] 2 plots (54) and agree well with the nucleation rate constant obtained from NEF-fits of the full progress curve (see Table 2).

Ligand docking
Aβ 42 and ligands were semi-randomly (82) positioned in a 5.0 × 5.0 × 5.0 nm cube of water, PO 4 (50 mM), and KCl (0.10 M) at pH 7.4, 298 K with the constraint that the smallest inter-atom distance between the two structures was ≥5 Å.The ligand was thermally equilibrated in 100 ps increments, and the energy-ofinteraction was calculated over 20 ns using g_energy.Binding free energies were calculated by subtracting the energy-ofinteraction of the ligand-bound Aβ 42 from the sum of the individual ligand and peptide interaction energies (32,33).The Aβ 42 oligomerization mechanism 10 nm cube of water, PO 4 (50 mM), and KCl (0.10 M) at pH 7.4, 298 K, with the constraint that the smallest inter-atom distance between the two structures was ≥10 Å.Each Aβ 42 CH cluster was maintained within its cluster by a weak restraining force (0.50 kJ/mole) that switched to 0 kJ/mole once the monomer/monomer interaction energy rose to one 10th the energy needed to separate monomers in an oligomer (25 kJ per mole) (64).The systems were thermally equilibrated in 100 ps increments and simulations were run for 5.0 μs.

Aβ 42 oligomerization
Eight Aβ 42 CS monomers, obtained from docking studies, were semi-randomly positioned in a 10 × 10 × 10 nm cube containing water, PO 4 (50 mM), and KCl (0.10 M), pH 7.4, 298 K, with the constraint that the smallest inter-atom distance between any two structures was ≥10 Å.The system was thermally equilibrated in 100-ps increments and the simulation was run for 50 ns.

Aβ 42 fragmentation
A 25-mer was constructed by "stitching together" and energy-minimizing 8-mers obtained from the oligomerization studies.A 25-mer Aβ 42 CS fibril was placed in a 20 × 20 × 20 nm cube of water, PO 4 (50 mM), and KCl (0.10 M), pH 7.4, 298 K.The system was thermally equilibrated in 100 ps increments and the simulation was run for 500 ns.Fragmentation was monitored by increased solvent exposure at the subunit interfaces.
(see Methods).An Aβ 42 titration of DHE is presented in Figure 1A.The titration data were least-squares fit to a single-binding-site model and the resulting best fit (indicated by the solid line) predicts a K d of 16 ± 1 nM and a 4.4 ± 0.2-fold increase in DHE fluorescence at saturation.The stoichiometry of the Aβ 42 DHE complex was determined in a second titration, Figure 1B, in which DHE is held fixed and saturated at 63 × K d (1.0 μM).Under this condition, Aβ 42 essentially quantitatively binds DHE until its concentration exceeds that of DHE, which results in a breakpoint in the titration curve that yields the stoichiometry.The arrow seen descending from the breakpoint indicates a stoichiometry of 1:1, which agrees well with the 1:1 CH-metabolite:Aβ stoichiometry estimated from analysis of senile plaques microdissected from AD-patient brain tissue (15).CH and CS affinities were determined in competitivebinding studies in which DHE is progressively displaced by titration of the non-fluorescent ligand, Figure 1, C and D. CH and CS were titrated into an equilibrated solution containing Aβ 42 (20 nM, 1.3 × K d ) and DHE (10 nM, 0.67 × K d ).Data were fit to a competitive single-binding-site model (32-34) (see Methods, Sterol binding to Aβ 42 -Equilibrium studies).The best-fit results are shown as solid lines passing through the data and predict CS and CH dissociation constants of 36 ± 3 and 120 ± 10 nM, respectively (see
) indicate ≤2% Aβ 42 oligomerization.The Figure 1, C and D titrations required a shorter measurement time due to the acceleration of oligomerization caused by CS and CH (discussed below).The measurement time interval was reduced to <5 min by using freshly prepared solutions for each data point in the titration.Control progress curves (Fig. S1, C and D) indicate ≤2% Aβ 42 oligomerized at the 5 min time-point.Pre-steady state binding studies To establish the rates at which Aβ 42 ligand complexes form and dissociate, the rate constants governing the binding reactions were determined.DHE binding was monitored in real time using a stopped-flow fluorimeter via binding-induced changes in DHE fluorescence.A representative bindingreaction progress curve is presented in Figure 2A.The reactions are pseudo first order in [ligand] and k obs was obtained by least-squares fitting progress curves to a single-exponential equation (44, 45).k obs values were determined (in triplicate) at a series of Aβ 42 concentrations and the averaged values are plotted versus [Aβ 42 ] in Figure 2B.k on and k off are given by the slope and intercept of the k obs -versus-[Aβ 42 ] plot obtained by linear least-square fitting (44, 45).CH and CS k off values were determined in competitive stopped-flow fluorescence studies in which CH or CS (8.5 × K d , post mixing) is 98% displaced by DHE (330 × K d , post mixing) -Figure 2, C and D. Under these conditions, the displacement reactions are irreversible first-order and k off values are obtained by least-squares fitting to a single-exponential equation.k on values were calculated using k off and the corresponding K eq values.The rate constants are compiled in Table

Figure 2 .
Figure 2. Sterol binding to Aβ 42 -pre-steady state studies.A, DHE binding.Reactions were monitored via binding induced changes in DHE fluorescence using a stopped-flow fluorimeter (λ ex = 325, λ em > 400 nm).Fluorescence intensity, I, is reported relative to the intensity in the absence of ligand, I o .A solution containing Aβ 42 (2.0 μM, 74 × K d ), K 2 PO 4 (50 mM), pH 7.4, 25 C ± 2 deg.C was rapidly mixed (1:1, v/v) with a solution identical except that Aβ 42 was replaced by DHE (40 nM, 2.7 × K d ).The bindingreaction curve shown is the average of five independent progress curves.The averaged curve was a least-squares fit to a single-exponential equation and the resulting best fit (indicated by the red line) yielded k obs .B, DHE k on and k off .k obs values obtained as in Panel A were determined in triplicate at varying Aβ 42 concentrations and the averaged values are shown plotted versus [Aβ 42 ].k on and k off are given by the slope and intercept of a linear least-squares fit of the k obs versus [Aβ 42 ] plot.C and D, CH and CS displacement reactions.A solution containing DHE (10 μM, 630 × K d ), K 2 PO 4 (50 mM), pH 7.5, 25 C ± 2 deg.C was rapidly mixed (1:1, v/v) with a solution in which DHE was replaced with Aβ 42 (0.10 μM, 0.83 × K d ) and CH (2.0 μM, 17 × K d ), Panel C, or, Aβ 42 (0.10 μM, 2.9 × K d ) and CS (0.60 μM, 17 × K d ), Panel D. The final DHE concentration (5.0 μM, 330 × K d ) displaces 98 % of either CH (1.0 μM, 8.3 × K d ) or CS (0.30 μM, 8.3 × K d ); hence, the dissociation reactions are pseudo first order.k off was obtained from a least-squares fit to a single-exponential equation (shown as red line passing through the data).

Figure 5 .
Figure 5. MD-predicted Aβ 42 monomer structures.A, the CHAβ 42 monomer.B, the CSAβ 42 monomer.All residues in direct contact with the ligand are shown in "stick" and labeled.Small red spheres mark the Aβ 42 peptide C-terminal residue, A42.

Figure 6 .
Figure 6.Dimerization studies.A and B, dimerization is monomer dependent.Eight monomer forms (unliganded peptide, CHpeptide Forms 1-6, and CSpeptide) were tested in MD simulations for their tendency to form dimers over a 5.0 μs time interval.Panel A presents progress curves for the species that formed dimersi.e., CSpeptide (CS), Form 3 CHpeptide (CH), and unliganded peptide.Panel B shows the progress curves for CH Forms that did not yield dimers.The curves are numbered according to the CH Forms given in Fig. S2.C-F, dimer structures.Panels C-E present the time average of the structures in the plateaus of the CS, CH, and unliganded-peptide progress curves, respectively.Panel F presents the structure of the unliganded-peptide intermediate that rapidly forms and slowly rearranges to the structure seen in Panel E.

Figure 7 .
Figure 7. CSAβ 42 oligomerization studies.A, CSAβ 42 octamer assembly.Eight CSAβ 42 monomers are seen spontaneously assembling into an octamer.Black and red lines trace the oligomerization status of the two peptides that initiate oligomerization.The simulation was initiated with eight monomers randomly positioned in a 10 × 10 × 10 nm cube of water, PO 4 (50 mM), KCl (0.10 mM), pH 7.4, 25 C. B, interface formation.Each progress curve shows the transition of two interface-forming species from an earlycontact stage to a fully formed interface.The seven transitions associated with octamer assembly are included in the figure.The curves are separated based on reaction rate into two classesdimer interface formation, and oligomer interface formation (which includes monomer/oligo and oligo/oligo interfaces).The progress curves in each class were least-squares fit to a single exponential equation, the best-fit k obs values within each class were averaged and the average value was used to generate the solid lines seen passing through the datasets.C, predicted structure of the CS octamer.

where C = 1 +
([DHE]/K d DHE ), [L] and K d L are concentrations and affinities associated with CS or CH, and I max is the fluorescence change associated with displacement of all peptidebound DHE.I max = (fraction DHE-bound to peptide at zero competitive ligands)/4.4thefold fluorescence change associated with DHE dissociation, see Figure 1A.Sterol binding to Aβ 42 -Pre-steady state studies Pre-steady-state binding of sterols to Aβ 42 was monitored via the binding-induced change in DHE fluorescence (λ ex = 325, λ em > 400 nm) using an Applied Photophysics SX20 stopped-flow fluorimeter.DHE binding-Progress curves were obtained by rapidly mixing (1:1 v/v) a solution containing DHE (0.50 μM, 33 × K d ) and K 2 PO 4 (50 mM), pH 7.4, 25 C ± 2 deg.C, with a solution that was identical except that it contained Aβ 42 (0.30-4.0 μM, 20-260 × K d ).Three progress curves (each an average of five independently obtained curves) were collected at five separate Aβ 42 concentrations.The observed rate constant (k obs ) at a given [Aβ 42 ] was obtained by fitting the average of the three curves to a single-exponential equation using Pro-K software (75).k on and k off were obtained from the slopes and intercepts predicted by linear least-squares analysis of k obs versus [Aβ 42 ] plots.CH and CS binding-Progress curves were obtained by rapidly mixing (1:1 v/v) a solution containing Aβ 42 (10 nM), CH (2.0 μM, 16 × K d ) or CS (600 nM, 17 × K d ), K 2 PO 4 (50 mM), pH 7.4, 25 C ± 2 deg.C, with a solution containing DHE (2.5 μM, 160 × K d ), K 2 PO 4 (50 mM), pH 7.4, 25 C ± 2 deg.C. The post-mixing DHE concentration displaces 97.5% of CH or CS from Aβ 42 ; hence, the displacement reactions are pseudo-first order.Progress curves were determined in triplicate and k off was obtained by least-squares fitting the averaged curves to a single-exponential equation using Pro-K.Aβ-fibril formation Fibril formation was monitored via the binding-induced change in ThT fluorescence (λ ex = 450 nm, λ em = 482 nm) (76).Reaction conditions: Aβ 42 (1.0 μM), ThT (30 μM), ligand (CH (3.0 μM, 17 × K d ) or CS (1.6 μM, 17 × K d ) or no ligand), DMSO (0.50 % v/v), K 2 PO 4 (50 mM), pH 7.4, 25 C ± 2 deg.C. Reagents (peptide, CH, CS, and ThT) were prepared immediately prior to use.CH and CS were solubilized in neat DMSO.Progress curves were determined in triplicate, and data were fit using the Nucleation-Fragmentation-Elongation (NEF) model (see Results and discussion).

Table 1
Sterol binding to Aβ 42 a Molecular-dynamics predicted values.b Parenthesises enclose one standard deviation.c Determined in DHE competition studies.d Determined in DHE displacement studies.e Calculated by dividing k off by K d .