Molecular determinants of Aβ₄₂ adsorption to amyloid fibril surfaces

Abstract

The long lag times and subsequent rapid growth of Alzheimer’s Aβ₄₂fibrils can be explained by a secondary nucleation step, in which existing fibril surfaces are able to nucleate formation of new fibrils via an autocatalytic process. The molecular mechanism of secondary nucleation, however, is still unknown. Here we investigate the first step, namely adsorption of the Aβ₄₂ peptide monomers onto the fibril surface. Using long all-atom molecular simulations and an enhanced sampling scheme, we are able to generate a diverse ensemble of binding events. The resulting thermodynamics of adsorption are consistent with experiment, as well as with the requirements for effective autocatalysis determined from coarse-grained simulations. We identify the key interactions stabilizing the adsorbed state, which are predominantly polar in nature, and relate them to the effects of known disease-causing mutations.

Graphical Abstract

The most common form of dementia is Alzheimer’s Disease (AD), which is related at the cellular and clinical levels to neuropathy and subsequent psychiatric decline involving loss of memory, cognition and motor control. At the present time, this ultimately fatal disease has no cure and is poised to present an intense challenge to a globally aging population. In the United States, for example, it has been predicted that the prevalence of the disease could reach 16 million and could cost $1.1 trillion by 2050.¹ At the molecular level, AD has been correlated with the aggregation of the Aβ peptide into amyloid fibrils, which ultimately constitute the insoluble extracellular plaques found in patient autopsies.^2,3 Note that Aβ oligomers have also been implicated in the disease, and there is evidence that they are more toxic than the fibrils.^4–7 In vitro, amyloid fibril formation is characterized by a long lag phase, followed by rapid growth, which can be quantitatively described by a kinetic model involving both primary nucleation and elongation of fibrils, as well as secondary nucleation.^8–10 In secondary nucleation, the surfaces of existing amyloid fibrils catalyze the nucleation of new aggregates; in fact this is how the majority of new oligomers are produced.¹¹ This process gains added significance with the recognition that it may be small soluble oligomeric species produced en route to assembly that are toxic in humans, rather than the final fibrillar aggregates themselves.^12–14 In support of this theory, there is evidence that selectively blocking secondary nucleation results in a steep reduction of toxicity in cell and in worm models.^15–17

Despite the clear medical importance of secondary nucleation, the molecular details of the process remain unclear as it has only been possible to draw macroscopic inferences about this reaction from experiment, using bulk chemical kinetics. Simulation models using phenomenological coarse-grained models have been able to provide insights into the general nature of the reaction: a fine balance between peptide-peptide and peptide-fibril affinity is necessary if secondary nucleation is to be dominant, and there should be a conformational rearrangement within the peptide for detachment from the fibril to occur.¹⁸ All-atom computational approaches could potentially provide additional predictive insights into the reaction mechanism as they over a level of resolution inaccessible to experiments. As a first step towards understanding the molecular mechanism of secondary nucleation, we have studied the adsorption of Aβ₄₂peptides onto fibrils using all-atom molecular simulations in explicit solvent.

In our simulations, we model the fibril based on a structure of the Aβ₄₂fibril recently determined by solid-state NMR.¹⁹ We explicitly include 10 layers of peptides, but the fibril is infinitely replicated in the z direction through an appropriate choice of periodic boundaries. An additional free Aβ₄₂ monomer is included to interact with the fibril, as well as 150 mM NaCl and explicit water. To ensure that our simulations were physically accurate, we took steps to address the two main limitations of all-atom simulations: the force field^20,21 and sampling problems. We chose to use the Amber03ws force field, which has been shown to describe well the behaviors of intrinsically disordered peptides,^22–25 in particular single-molecule measurements of the Aβ₄₂ monomer.²⁶ Long equilibrium simulations alone are unable to sample a wide variety of protein-protein binding interactions, as the time scale for dissociation is long compared to that accessible in simulation, such that complexes become kinetically trapped in the first stable encounter pose they find. We therefore used a novel Hamiltonian replica exchange enhanced sampling scheme in which 16 parallel simulations were run, each differing slightly in the protein-solvent interaction energy, controlled by a parameter λ. When λ is low, peptide-fibril binding is favored, while the highest λ values favor dissociation. This scheme is similar to one that has been used to study cryptic binding pockets in folded proteins,²⁷ though here it is applied to an intrinsically disordered peptide. As with temperature replica-exchange schemes, configurations between neighboring windows are periodically exchanged based on a Metropolis criterion, such that the peptide is encouraged to come on and off the fibril several times, allowing us to sample a range of binding modes at equilibrium. We have verified that the fibril is stable in this scheme, by computing the fraction of monomer-monomer contacts that would be present in the experimental structure, as a function of time. As can be seen in Fig. S2, this is stable over the course of the simulation. This sampling scheme is summarized in Fig 1(b), showing schematics of the solvation state of the monomer as a function of λ, which controls the hydrophilicity or proteophilicity of the system. Fig. 1(c) shows a representative trajectory of a continuous simulation (one that has been followed through λ swaps), and demonstrates that this scheme allows us to sample several independent binding and unbinding events (as measured by the minimum distance between fibril and peptide atoms r_min), and that the the peptide-fibril contacts fluctuate while bound. To test the extent of our sampling, we ran two independent 16-copy simulations of our system started from different initial conditions: one in which the peptide was already in contact with the fibril, and the other in which it was free in solution.

Figure 1:

Simulation setup. (a) Starting configuration for one of the independent simulations, with the infinite Aβ₄₂ fibril shown in gray, the Aβ₄₂ monomer in red, water molecules as translucent red and white spheres, sodium ions as translucent violet spheres and chloride ions as translucent green spheres. (b) Schematic view of the Hamiltonian replica exchange enhanced sampling scheme, in which several parallel simulations run, each with a protein water interaction energy scaled by a factor λ_i, resulting in low λ windows favoring peptide adsorption and high λ windows favoring peptide solvation. Protein-water interactions are depicted schematically by a star of increasing size. (c) Representative fibril-peptide minimum distance (top) and number of contacts (bottom) trajectories, where the simulations have been followed through exchanges and hence made geometrically continuous. Gray curves are raw data, solid colors are moving averages over 7.5 ns windows and horizontal dashed line defines the bound state.

A fundamental parameter characterizing fibril-peptide association is the binding free energy. To obtain this from the simulations, we compute the free energy surface as a function of the order parameter r_min. We use r_min rather than, for example, the distance between centers of mass, because it is able to discriminate clearly whether or not the fibril and peptide species are in contact. This free energy (Fig. 2) shows that adsorption is spontaneous. Furthermore, the results from the two independent simulations are consistent with each other. The residual difference between the curves is due to the challenge of obtaining a representative sampling of the binding equilibrium. The free energy surfaces allow us to estimate a standard free energy of adsorption of Δ_blindG^⦵ = −19±2 kJ.mol⁻¹, averaged across both simulations. This value is quantitatively in line with experimental surface plasmon resonance measurements which give an estimate of Δ_blindG^⦵ = −27 kJ.mol⁻¹.²⁸ Our access to all-atom energies also allows us to estimate the standard enthalpy of adsorption as Δ_blindH^⦵ = −90 ± 40 kJ.mol⁻¹, implying an entropic contribution to adsorption of −TΔ_blindS^⦵ = 70 ± 40 kJ.mol⁻¹. These results are in reasonable agreement with the corresponding experimental estimates, although the errors on the enthalpic and entropic components are large (Table 1). In our work we have used a force field with specifically tuned protein-water interactions, since our work and that of others had suggested that protein-protein interactions were too favourable in standard force fields.^22,29,30 An extrapolation of the adsorption free energy from the different λ windows sampled to λ = 1.0 (corresponding to a more standard force field, Amber ff03w^31,32) suggests that binding would be significantly tighter (Fig. S4).

Figure 2:

Peptide adsorption free energy surfaces, with gray curves showing results for each individual simulation and the red curve showing the Boltzmann average. Shadings denote standard errors and vertical dashed line defines the bound state. These curves were calculated at the simulation monomer concentration, then corrected to a standard state concentration of c^⦵ = 1 M to yield the values shown in Table 1.

Table 1:

Thermodynamics of Aβ₄₂ peptide-fibril adsorption. All values are in units of kJ.mol⁻¹ and refer to a standard state of 1 M monomer and T = 300 K.

	ΔbindG⦵	ΔbindH⦵	TΔbindS⦵
Simulation	−19 ± 2	−90 ± 40	70 ± 40
Experiment28	−27	−67	40

Our value for the binding energy is also consistent with coarse-grained molecular simulations, from which it was concluded that a binding energy on the order of 20 kJ.mol⁻¹ results in maximally efficient autocatalysis.¹⁸ This optimal interaction strength is reminiscent of the Sabatier principle of inorganic heterogeneous catalysis, which states that the the affinity between a catalyst and its substrate should be favorable, but not overly so, for efficient catalytic turnover.³³

Encouraged by our ability to reproduce experimental binding thermodynamics, we went on to investigate in more detail the molecular interactions stabilizing binding. The numbers of intermolecular contacts formed by each residue of the fibril and the peptide (Fig. 3) reveal that there are definite interaction hotspots on the fibril, including residues Gln 15 and Lys 16. In contrast, the peptide is more promiscuous in binding, albeit with elevated contact probabilities at the termini and the residues Glu 22 and Asp 23. To obtain representative major binding motifs, we performed a cluster analysis of the intermolecular contact maps. This revealed that the largest cluster is characterized by interactions between the positive Lys 16 of the fibril surface and the negative Glu 22, Asp 23 and Ala 42 carboxyl group of the peptide. The next two important clusters also showed largely polar interactions between charged sidechains and between hydrogen bond donors and acceptors. The favorable charged and polar interactions between peptide and fibril suggest that salt should modulate the binding affinity, and reweighting our simulations using a Debye-Hückel model for screening suggests that binding is indeed tighter at lower ionic strength (Fig. S5) – in spite of the long-range repulsion between peptide and fibril due to their net charge. In our work, we focussed on a single filament model of the Aβ₄₂ fibril, partly as we were already at the limit of what is computationally feasible. Several subsequent structural studies have found that Aβ₄₂ fibrils consist of two filaments related by an approximately two-fold symmetry axis.^34–36 Nonetheless, most of the fibril residues interacting with the peptide are not in regions involved in binding the symmetry-related fiber, a prominent exception being Gln-15, which does form contacts with the neighbouring fiber. In addition, it should be noted that although the structures determined experimentally are generally in good agreement, there may be some dependence on the chosen structure, which should be investigated in future work.

Figure 3:

Peptide-fibril contact analysis. (a) Probabilities of individual amino acids being involved in adsorption interactions in (top) the fibril surface and (bottom) the peptide. Translucent curves are results from the independent simulations, full colored curves are averages and error bars are standard errors. (b) Structural visualization of adsorption hotspots on the fibril, with the color of the amino acid getting more red as the residue is more likely to be involved. Translucent fibril shows approximate location of second protofibril in a C₂ symmetric arrangement, as suggested is appropriate for Aβ₄₂ fibrils by other structural studies.^34–36 (c) Clustering analysis of binding modes showing top three interaction motifs, with colored bar denoting statistical weight of each cluster and inset structures showing structures closest to cluster centroids. N-termini shown as spheres, and all figures made using PyMOL.

Interestingly, the residues Glu 22 and Asp 23 that we identify in our analysis of intermolecular contacts are those that are mutated to neutral ones in the familial Aβ Iowa, Dutch and Arctic mutations. These mutations result in clinical phenotypes similar to Alzheimer’s Disease, often accompanied by cerebral hemorrhage, and in vitro have been found to accelerate Aβ aggregation.^37–40 These observations may be explained if desorption were rate-limiting in secondary nucleation, such that destabilizing the monomer-fibril interaction would result in faster turnover, though the mutations could very well affect other determinants of aggregation such as monomer β-propensity or inter-peptide interactions. Rate-limiting detachment has, however, been observed in vitro for Aβ₄₂ at high salt concentrations or low pH conditions.^41,42 Furthermore Lys 16, the major fibril residue identified in our analysis, has also been shown to be a key residue in the aggregation process, with K16A mutants showing delayed fibril formation and reduced cytotoxicity.⁴³ Our finding that peptide adsorption is mediated by polar interactions is in contrast with results from other molecular simulation studies, which have found that hydrophobic interactions dominate. Most of these studies have focused on Aβ₄₀;^44,45 a recent paper, however, also found that an Aβ₁₋₄₂ monomer interacts with a truncated Aβ₁₇₋₄₂ fibril polymorph with structure modelled on that of an Aβ₄₀ fibril through hydrophobic contacts.⁴⁶ The main difference from our work in all of these studies is that they are based on the structure of an Aβ₄₀ fibril, either because they were concerned with that peptide, or because they were done before an experimental structure of Aβ₄₂ was published. This is the most likely reason for any differences regarding which residues are important. An additional factor may be that the force field we use, which is optimized for protein-protein interactions, is significantly less hydrophobic overall. The adsorption mechanism involving polar interactions which we observe does, however, appear most consistent with the experimental enthalpy-driven binding thermodynamics in which the positive value of −TΔ_bindS suggests that the hydrophobic effect is not the major driving force of adsorption.²⁸

We also examined the effect that adsorption has on the monomer configuration by building the intramolecular contact maps shown in Fig. 4(a). As demonstrated by the similarity in the free and bound states, adsorption is accompanied by only modest structural changes in the monomer. This suggests that interactions with other adsorbed peptides may be necessary for formation of ordered structure in secondary nuclei, although it is also possible that structural conversion could occur in the monomer on a longer time scale than is accessible in our simulations. The small amount of local structure formation induced by adsorption appears to be due to formation of β-hairpins (Fig. 4(b)). We confirmed that adsorption was in fact related to the appearance of β structure from the average increase population (≈2–3 % per residue) of residues assigned to β-sheet secondary structure.

Figure 4:

Effect of adsorption on monomer configuration. (a) Intramolecular contact maps for free (upper triangle) and bound (lower triangle) monomers. (b) Difference contact map between bound and free states.

While initial adsorption of monomers to a fibril is clearly only part of the secondary nucleation mechanism, we can nonetheless ask to which mutations it would be most sensitive. How can the adsorption mechanism proposed be tested experimentally? One of the most powerful tools for dissecting protein interactions is site-directed mutagenesis. We therefore designed appropriate mutants by assessing the effect of residue substitutions after reweighting the configurations sampled in our trajectories using a simple contact potential, as described in the Supplementary Information. We chose only those constructs which are expected to reduce catalytic efficiency, either by decreasing or increasing the adsorption strength in accord with the Sabatier principle, while also being compatible with incorporation into the experimental fibril structure. Our analysis suggested several candidates, in particular mutations to residues 15, 16, 22, 23, 28, which should alter peptide-fibril interactions; it will be interesting to test the effect of mutations to these residues experimentally in the future.

In summary, we have used molecular simulations to probe at atomistic resolution the first step of Aβ₄₂ secondary nucleation, namely the adsorption of a monomer onto a fibril surface. The computed thermodynamic properties of binding quantitatively match experimental measures, and are consistent with estimates from coarse-grained simulations of the most efficient binding energy for autocatalysis. In addition, the structural detail of our work has allowed us to identify major binding modes of adsorption, which mostly consist of polar interactions, involving particularly the fibril residue Lys 16 and the peptide residues Glu 22 and Asp 23. These are all residues which have been identified as critical to the aggregation process either by in vitro studies or through patient mutations, providing further evidence that our simulations capture the correct binding mechanism. In principle, our work can also be used to design inhibitors targeting the interactions between the fibril and peptide.