The Levinthal Problem in Amyloid Aggregation: Sampling of a Flat Reaction Space

Competing addition processes give distinct growth regimes in the assembly of 1D filaments

We present a model to describe the concentration-dependent growth of protein filaments. Our model contains two states, a low-entropy/high-affinity ordered state and a high-entropy/low-affinity disordered state. Consistent with experiments, our model shows a diffusion-limited linear growth regime at low concentration, followed by a concentration-independent plateau at intermediate concentrations, and rapid disordered precipitation at the highest concentrations. We show that growth in the linear and plateau regions is the result of two processes that compete amid the rapid binding and unbinding of nonspecific states. The first process is the addition of ordered molecules during periods in which the end of the filament is free of incorrectly bound molecules. The second process is the capture of defects, which occurs when consecutive ordered additions occur on top of incorrectly bound molecules. We show that a key molecular property is the probability that a diffusive collision results in a correctly bound state. Small values of this probability suppress the defect capture growth mode, resulting in a plateau in the growth rate when incorrectly bound molecules become common enough to poison ordered growth. We show that conditions that nonspecifically suppress or enhance intermolecular interactions, such as the addition of depletants or osmolytes, have opposite effects on the growth rate in the linear and plateau regimes. In the linear regime, stronger interactions promote growth by reducing dissolution events, but in the plateau regime stronger interactions inhibit growth by stabilizing incorrectly bound molecules.

The mechanism of amyloid fibril growth from Φ-value analysis

Amyloid fibrils are highly stable misfolded protein assemblies that play an important role in several neurodegenerative and systemic diseases. Although structural information of the amyloid state is now abundant, mechanistic details about the misfolding process remain elusive. Inspired by the Φ-value analysis of protein folding, we combined experiments and molecular simulations to resolve amino-acid contacts and determine the structure of the transition-state ensemble-the rate-limiting step-for fibril elongation of PI3K-SH3 amyloid fibrils. The ensemble was validated experimentally by Tanford β analysis and computationally by free energy calculations. Although protein folding proceeds on funnel-shaped landscapes, here we find that the energy landscape for the misfolding reaction consists of a large 'golf course' region, defined by a single energy barrier and transition state, accessing a sharply funnelled region. Thus, misfolding occurs by rare, successful monomer-fibril end collisions interspersed by numerous unsuccessful binding attempts. Taken together, these insights provide a quantitative and highly resolved description of a protein misfolding reaction.

Distinct growth regimes of α-synuclein amyloid elongation

Addition of amyloid seeds to aggregation-prone monomers allows for amyloid fiber growth (elongation) omitting slow nucleation. We here combine Thioflavin T fluorescence (probing formation of amyloids) and solution-state NMR spectroscopy (probing disappearance of monomers) to assess elongation kinetics of the amyloidogenic protein, α-synuclein, for which aggregation is linked to Parkinson's disease. We found that both spectroscopic detection methods give similar kinetic results, which can be fitted by applying double exponential decay functions. When the origin of the two-phase behavior was analyzed by mathematical modeling, parallel paths as well as stop-and-go behavior were excluded as possible explanations. Instead, supported by previous theory, the experimental elongation data reveal distinct kinetic regimes that depend on instantaneous monomer concentration. At low monomer concentrations (toward end of experiments), amyloid growth is limited by conformational changes resulting in β-strand alignments. At the higher monomer concentrations (initial time points of experiments), growth occurs rapidly by incorporating monomers that have not successfully completed the conformational search. The presence of a fast disordered elongation regime at high monomer concentrations agrees with coarse-grained simulations and theory but has not been detected experimentally before. Our results may be related to the wide range of amyloid folds observed.

Beneficial and detrimental effects of non-specific binding during DNA hybridization

DNA strands have to sample numerous states to find the alignment that maximizes Watson-Crick-Franklin base pairing. This process depends strongly on sequence, which affects the stability of the native duplex as well as the prevalence of non-native inter- and intramolecular helices. We present a theory that describes DNA hybridization as a three-stage process: diffusion, registry search, and zipping. We find that non-specific binding affects each of these stages in different ways. Mis-registered intermolecular binding in the registry search stage helps DNA strands sample different alignments and accelerates the hybridization rate. Non-native intramolecular structure affects all three stages by rendering portions of the molecule inert to intermolecular association, limiting mis-registered alignments to be sampled, and impeding the zipping process. Once in-register base pairs are formed, the stability of the native structure is important to hold the molecules together long enough for non-native contacts to break.

Self-Assembly of Amyloid Fibrils into 3D Gel Clusters versus 2D Sheets

The deposition of dense fibril plaques represents the pathological hallmark for a multitude of human disorders, including many neurodegenerative diseases. Fibril plaques are predominately composed of amyloid fibrils, characterized by their underlying cross beta-sheet architecture. Research into the mechanisms of amyloid formation has mostly focused on characterizing and modeling the growth of individual fibrils and associated oligomers from their monomeric precursors. Much less is known about the mechanisms causing individual fibrils to assemble into ordered fibrillar suprastructures. Elucidating the mechanisms regulating this "secondary" self-assembly into distinct suprastructures is important for understanding how individual protein fibrils form the prominent macroscopic plaques observed in disease. Whether and how amyloid fibrils assemble into either 2D or 3D supramolecular structures also relates to ongoing efforts on using amyloid fibrils as substrates or scaffolds for self-assembling functional biomaterials. Here, we investigated the conditions under which preformed amyloid fibrils of a lysozyme assemble into larger superstructures as a function of charge screening or pH. Fibrils either assembled into three-dimensional gel clusters or two-dimensional fibril sheets. The latter displayed optical birefringence, diagnostic of amyloid plaques. We presume that pH and salt modulate fibril charge repulsion, which allows anisotropic fibril-fibril attraction to emerge and drive the transition from 3D to 2D fibril self-assembly.

Conformational entropy limits the transition from nucleation to elongation in amyloid aggregation

The formation of β-sheet rich amyloid fibrils in Alzheimer's disease and other neurodegenerative disorders is limited by a slow nucleation event. To understand the initial formation of β-sheets from disordered peptides, we used all-atom simulations to parameterize a lattice model that treats each amino acid as a binary variable with β and non-β states. We show that translational and conformational entropy give the nascent β-sheet an anisotropic surface tension which can be used to describe the nucleus with two-dimensional Classical Nucleation Theory. Since translational entropy depends on concentration, the aspect ratio of the critical β-sheet changes with protein concentration. Our model explains the transition from the nucleation phase to elongation as the point where the β-sheet core becomes large enough to overcome the conformational entropy cost to straighten the terminal molecule. At this point the β-strands in the nucleus spontaneously elongate, which results in a larger binding surface to capture new molecules. These results suggest that nucleation is relatively insensitive to sequence differences in co-aggregation experiments because the nucleus only involves a small portion of the peptide.

Examining the Ensembles of Amyloid-β Monomer Variants and Their Propensities to Form Fibers Using an Energy Landscape Visualization Method

The amyloid-β (Aβ) monomer, an intrinsically disordered peptide, is produced by the cleavage of the amyloid precursor protein, leading to Aβ-40 and Aβ-42 as major products. These two isoforms generate pathological aggregates, whose accumulation correlates with Alzheimer's disease (AD). Experiments have shown that even though the natural abundance of Aβ-42 is smaller than that for Aβ-40, the Aβ-42 is more aggregation-prone compared to Aβ-40. Moreover, several single-point mutations are associated with early onset forms of AD. This work analyzes coarse-grained associative-memory, water-mediated, structure and energy model (AWSEM) simulations of normal Aβ-40 and Aβ-42 monomers, along with six single-point mutations associated with early onset disease. We analyzed the simulations using the energy landscape visualization method (ELViM), a reaction-coordinate-free approach suited to explore the frustrated energy landscapes of intrinsically disordered proteins. ELViM is shown to distinguish the monomer ensembles of variants that rapidly form fibers from those that do not form fibers as readily. It also delineates the amino acid contacts characterizing each ensemble. The results shed light on the potential of ELViM to probe intrinsically disordered proteins.

Insight Into Seeded Tau Fibril Growth From Molecular Dynamics Simulation of the Alzheimer's Disease Protofibril Core

Aggregates of the microtubule associated tau protein are a major constituent of neurofibrillary lesions that define Alzheimer’s disease (AD) pathology. Increasing experimental evidence suggests that the spread of tau neurofibrillary tangles results from a prion-like seeding mechanism in which small oligomeric tau fibrils template the conversion of native, intrinsically disordered, tau proteins into their pathological form. By using atomistic molecular dynamics (MD) simulations, we investigate the stability and dissociation thermodynamics of high-resolution cryo-electron microscopy (cryo-EM) structures of both the AD paired-helical filament (PHF) and straight filament (SF). Non-equilibrium steered MD (SMD) center-of-mass pulling simulations are used to probe the stability of the protofibril structure and identify intermolecular contacts that must be broken before a single tau peptide can dissociate from the protofibril end. Using a combination of exploratory metadynamics and umbrella sampling, we investigate the complete dissociation pathway and compute a free energy profile for the dissociation of a single tau peptide from the fibril end. Different features of the free energy surface between the PHF and SF protofibril result from a different mechanism of tau unfolding. Comparison of wild-type tau PHF and post-translationally modified pSer356 tau shows that phosphorylation at this site changes the dissociation free energy surface of the terminal peptide. These results demonstrate how different protofibril morphologies template the folding of endogenous tau in distinct ways, and how post-translational modification can perturb the folding mechanism.

Amyloid assembly is dominated by misregistered kinetic traps on an unbiased energy landscape

Atomistic description of protein fibril formation has been elusive due to the complexity and long time scales of the conformational search. Here, we develop a multiscale approach combining numerous atomistic simulations in explicit solvent to construct Markov State Models (MSMs) of fibril growth. The search for the in-register fully bound fibril state is modeled as a random walk on a rugged two-dimensional energy landscape defined by β-sheet alignment and hydrogen-bonding states, whereas transitions involving states without hydrogen bonds are derived from kinetic clustering. The reversible association/dissociation of an incoming peptide and overall growth kinetics are then computed from MSM simulations. This approach is applied to derive a parameter-free, comprehensive description of fibril elongation of Aβ_16-22 and how it is modulated by phenylalanine-to-cyclohexylalanine (CHA) mutations. The trajectories show an aggregation mechanism in which the peptide spends most of its time trapped in misregistered β-sheet states connected by weakly bound states twith short lifetimes. Our results recapitulate the experimental observation that mutants CHA19 and CHA1920 accelerate fibril elongation but have a relatively minor effect on the critical concentration for fibril growth. Importantly, the kinetic consequences of mutations arise from cumulative effects of perturbing the network of productive and nonproductive pathways of fibril growth. This is consistent with the expectation that nonfunctional states will not have evolved efficient folding pathways and, therefore, will require a random search of configuration space. This study highlights the importance of describing the complete energy landscape when studying the elongation mechanism and kinetics of protein fibrils.

Theory of Sequence Effects in Amyloid Aggregation

We present a simple model for the effect of amino acid sequences on amyloid fibril formation. Using the HP model we find the binding lifetimes of four simple sequences by solving the first passage time for the intermolecular H-bond reaction coordinate. We find that sequences with identical binding energies have widely varying binding times depending on where the aggregation prone amino acids are located in the sequence. In general, longer binding times occur when the aggregation prone amino acids are clustered in a single "hot spot". Similarly, binding times are shortened by clustering weakly bound residues. Both of these effects are explained by an increase in the multiplicity of unbinding trajectories that comes from adding weak binding residues. Our model predicts a transition from ordered to disordered fibrils as the concentration of monomers increases. We apply our model to Aβ, IAPP, and apomyoglobin using binding energy estimates derived from bioinformatics. We find that these sequences are highly selective of the in-register state. This selectivity arises from the having strongly bound segments of varying length and separation.