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

The formation of amyloid fibrils has been associated with many neurodegenerative disorders, yet the mechanism of aggregation remains elusive, partly because aggregation time scales are too long to probe with atomistic simulations. A microscopic theory of fibril elongation was recently developed that could recapitulate experimental results with respect to the effects of temperature, denaturants, and protein concentration on fibril growth kinetics (Schmit, J. D. J. Chem. Phys. 2013, 138 (18), 185102). The theory identifies the conformational search over H-bonding states as the slowest step in the aggregation process and suggests that this search can be efficiently modeled as a random walk on a rugged one-dimensional energy landscape. This insight motivated the multiscale computational algorithm for simulating fibril growth presented in this paper. Briefly, a large number of short atomistic simulations are performed to compute the system diffusion tensor in the reaction coordinate space predicted by the analytic theory. Ensemble aggregation pathways and growth kinetics are then computed from Markov state model (MSM) trajectories. The algorithm is deployed here to understand the fibril growth mechanism and kinetics of Aβ_16-22 and three of its mutants. The order of growth rates of the wild-type and two single mutation peptides (CHA19 and CHA20) predicted by the MSM trajectories is consistent with experimental results. The simulation also correctly predicts that the double mutation (CHA19/CHA20) would reduce the fibril growth rate, even though the degree of rate reduction with respect to either single mutation is overestimated. This artifact may be attributed to the simplistic implicit solvent model. These trends in the growth rate are not apparent from inspection of the rate constants of individual bonds or the lifetimes of the mis-registered states that are the primary kinetic traps but only emerge in the ensemble of trajectories generated by the MSM.

Inhibitory effect of hydrophobic fullerenes on the β-sheet-rich oligomers of a hydrophilic GNNQQNY peptide revealed by atomistic simulations

Fullerenes suppress fibril-like β-sheet oligomers by interacting strongly with the nonpolar aliphatic groups of polar residues of GNNQQNY peptide, thus inhibit peptide aggregation.

Structural analysis of oligomeric and protofibrillar Aβ amyloid pair structures considering F20L mutation effects using molecular dynamics simulations

Aβ amyloid proteins are involved in neuro-degenerative diseases such as Alzheimer's, Parkinson's, and so forth. Because of its structurally stable feature under physiological conditions, Aβ amyloid protein disrupts the normal cell function. Because of these concerns, understanding the structural feature of Aβ amyloid protein in detail is crucial. There have been some efforts on lowering the structural stabilities of Aβ amyloid fibrils by decreasing the aromatic residues characteristic and hydrophobic effect. Yet, there is a lack of understanding of Aβ amyloid pair structures considering those effects. In this study, we provide the structural characteristics of wildtype (WT) and phenylalanine residue mutation to leucine (F20L) Aβ amyloid pair structures using molecular dynamics simulation in detail. We also considered the polymorphic feature of F20L and WT Aβ pair amyloids based on the facing β-strand directions between the amyloid pairs. As a result, we were able to observe the varying effects of mutation, polymorphism, and protofibril lengths on the structural stability of pair amyloids. Furthermore, we have also found that opposite structural stability exists on a certain polymorphic Aβ pair amyloids depending on its oligomeric or protofibrillar state, which can be helpful for understanding the amyloid growth mechanism via repetitive fragmentation and elongation mechanism. Proteins 2017; 85:580-592. © 2016 Wiley Periodicals, Inc.

Simulations of disordered proteins and systems with conformational heterogeneity

Intrinsically disordered proteins (IDPs) and protein regions can facilitate a wide variety of complex physiological processes such as binding, signaling, and formation of membraneless organelles. They can however also play pathological roles by aggregating into cytotoxic oligomers and fibrils. Characterizing the structure and function of disordered proteins is an onerous task, primarily because these proteins adopt transient structures, which are difficult to capture in experiments. Simulations have emerged as a powerful tool for interpreting and augmenting experimental measurements of IDPs. In this review we focus on computer simulations of disordered protein structures, functions, assemblies, and emerging questions that, taken together, give an overview of the field as it exists today.

Polymorphism of fibrillar structures depending on the size of assembled Aβ17-42 peptides

The size of assembled Aβ_17-42 peptides can determine polymorphism during oligomerization and fibrillization, but the mechanism of this effect is unknown. Starting from separate random monomers, various fibrillar oligomers with distinct structural characteristics were identified using discontinuous molecular dynamics simulations based on a coarse-grained protein model. From the structures observed in the simulations, two characteristic oligomer sizes emerged, trimer and paranuclei, which generated distinct structural patterns during fibrillization. A majority of the simulations for trimers and tetramers formed non-fibrillar oligomers, which primarily progress to off-pathway oligomers. Pentamers and hexamers were significantly converted into U-shape fibrillar structures, meaning that these oligomers, called paranuclei, might be potent on-pathway intermediates in fibril formation. Fibrillar oligomers larger than hexamers generated substantial polymorphism in which hybrid structures were readily formed and homogeneous fibrillar structures appeared infrequently.

Primary Fibril Nucleation of Aggregation Prone Tau Fragments PHF6 and PHF6

We performed replica exchange molecular dynamics and forward flux sampling simulations of hexapeptide VQIINK and VQIVYK systems, also known as, respectively, fragments PHF6* and PHF6 from the tau protein. Being a part of the microtubule binding region, these fragments are known to be aggregation prone, and at least one of them is a prerequisite for fibril formation of the tau protein. Using a coarse-grained force field, we establish the phase behavior of both fragments, and investigate the nucleation kinetics for the conversion into a β-sheet fibril. As the conversion is, in principle, a reversible process, we predict the rate constants for both the fibril formation and melting, and examine the corresponding mechanisms. Our simulations indicate that, while both fragments form disordered aggregates, only PHF6 is able to form β-sheet fibrils. This observation provides a possible explanation for the lack of available steric zipper crystal structures for PHF6*.

The Aggregation Free Energy Landscapes of Polyglutamine Repeats

Aggregates of proteins containing polyglutamine (polyQ) repeats are strongly associated with several neurodegenerative diseases. The length of the repeats correlates with the severity of the disease. Previous studies have shown that pure polyQ peptides aggregate by nucleated growth polymerization and that the size of the critical nucleus (n*) decreases from tetrameric to dimeric and monomeric as length increases from Q₁₈ to Q₂₆. Why the critical nucleus size changes with repeat-length has been unclear. Using the associative memory, water-mediated, structure and energy model, we construct the aggregation free energy landscapes for polyQ peptides of different repeat-lengths. These studies show that the monomer of the shorter repeat-length (Q₂₀) prefers an extended conformation and that its aggregation indeed has a trimeric nucleus (n* ∼ 3), while a longer repeat-length monomer (Q₃₀) prefers a β-hairpin conformation which then aggregates in a downhill fashion at 0.1 mM. For an intermediate length peptide (Q₂₆), there is an equal preference for hairpin and extended forms in the monomer which leads to a mixed inhomogeneous nucleation mechanism for fibrils. The predicted changes of monomeric structure and nucleation mechanism are confirmed by studying the aggregation free energy profile for a polyglutamine repeat with site-specific PG mutations that favor the hairpin form, giving results in harmony with experiments on this system.

Protein Aggregation and Molecular Crowding: Perspectives From Multiscale Simulations

Cells are extremely crowded environments, thus the use of diluted salted aqueous solutions containing a single protein is too simplistic to mimic the real situation. Macromolecular crowding might affect protein structure, folding, shape, conformational stability, binding of small molecules, enzymatic activity, interactions with cognate biomolecules, and pathological aggregation. The latter phenomenon typically leads to the formation of amyloid fibrils that are linked to several lethal neurodegenerative diseases, but that can also play a functional role in certain organisms. The majority of molecular simulations performed before the last few years were conducted in diluted solutions and were restricted both in the timescales and in the system dimensions by the available computational resources. In recent years, several computational solutions were developed to get close to physiological conditions. In this review we summarize the main computational techniques used to tackle the issue of protein aggregation both in a diluted and in a crowded environment.

Exploring the aggregation free energy landscape of the amyloid-β protein (1-40)

A predictive coarse-grained protein force field [associative memory, water-mediated, structure, and energy model for molecular dynamics (AWSEM)-MD] is used to study the energy landscapes and relative stabilities of amyloid-β protein (1-40) in the monomer and all of its oligomeric forms up to an octamer. We find that an isolated monomer is mainly disordered with a short α-helix formed at the central hydrophobic core region (L17-D23). A less stable hairpin structure, however, becomes increasingly more stable in oligomers, where hydrogen bonds can form between neighboring monomers. We explore the structure and stability of both prefibrillar oligomers that consist of mainly antiparallel β-sheets and fibrillar oligomers with only parallel β-sheets. Prefibrillar oligomers are polymorphic but typically take on a cylindrin-like shape composed of mostly antiparallel β-strands. At the concentration of the simulation, the aggregation free energy landscape is nearly downhill. We use umbrella sampling along a structural progress coordinate for interconversion between prefibrillar and fibrillar forms to identify a conversion pathway between these forms. The fibrillar oligomer only becomes favored over its prefibrillar counterpart in the pentamer where an interconversion bottleneck appears. The structural characterization of the pathway along with statistical mechanical perturbation theory allow us to evaluate the effects of concentration on the free energy landscape of aggregation as well as the effects of the Dutch and Arctic mutations associated with early onset of Alzheimer's disease.

Assembly of Triblock Amphiphilic Peptides into One-Dimensional Aggregates and Network Formation

Peptide assembly plays a key role in both neurological diseases and development of novel biomaterials with well-defined nanostructures. Synthetic model peptides provide a unique platform to explore the role of intermolecular interactions in the assembly process. A triblock peptide architecture designed by the Hartgerink group is a versatile system which relies on Coulomb interactions, hydrogen bonding, and hydrophobicity to guide these peptides' assembly at three different length scales: β-sheets, double-wall ribbon-like aggregates, and finally a highly porous network structure which can support gels with ≤1% by weight peptide concentration. In this study, by using molecular dynamics simulations of a structure based implicit solvent coarse grained model, we analyzed this hierarchical assembly process. Parametrization of our CG model is based on multiple-state points from atomistic simulations, which enables this model to represent the conformational adaptability of the triblock peptide molecule based on the surrounding medium. Our results indicate that emergence of the double-wall β-sheet packing mechanism, proposed in light of the experimental evidence, strongly depends on the subtle balance of the intermolecular forces. We demonstrate that, even though backbone hydrogen bonding dominates the early nucleation stages, depending on the strength of the hydrophobic and Coulomb forces, alternative structures such as zero-dimensional aggregates with two β-sheets oriented orthogonally (which we refer to as a cross-packed structure) and β-sheets with misoriented hydrophobic side chains are also feasible. We discuss the implications of these competing structures for the three different length scales of assembly by systematically investigating the influence of density, counterion valency, and hydrophobicity.

On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics

Simulated tempering (ST) is a generalized-ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass-scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.

Identification of Protein-Excipient Interaction Hotspots Using Computational Approaches

Protein formulation development relies on the selection of excipients that inhibit protein–protein interactions preventing aggregation. Empirical strategies involve screening many excipient and buffer combinations using force degradation studies. Such methods do not readily provide information on intermolecular interactions responsible for the protective effects of excipients. This study describes a molecular docking approach to screen and rank interactions allowing for the identification of protein–excipient hotspots to aid in the selection of excipients to be experimentally screened. Previously published work with Drosophila Su(dx) was used to develop and validate the computational methodology, which was then used to determine the formulation hotspots for Fab A33. Commonly used excipients were examined and compared to the regions in Fab A33 prone to protein–protein interactions that could lead to aggregation. This approach could provide information on a molecular level about the protective interactions of excipients in protein formulations to aid the more rational development of future formulations.

An Account of Amyloid Oligomers: Facts and Figures Obtained from Experiments and Simulations

The deposition of amyloid in brain tissue in the context of neurodegenerative diseases involves the formation of intermediate species-termed oligomers-of lower molecular mass and with structures that deviate from those of mature amyloid fibrils. Because these oligomers are thought to be primarily responsible for the subsequent disease pathogenesis, the elucidation of their structure is of enormous interest. Nevertheless, because of the high aggregation propensity and the polydispersity of oligomeric species formed by the proteins or peptides in question, the preparation of appropriate samples for high-resolution structural methods has proven to be rather difficult. This is why theoretical approaches have been of particular importance in gaining insights into possible oligomeric structures for some time. Only recently has it been possible to achieve some progress with regard to the experimentally based structural characterization of defined oligomeric species. Here we discuss how theory and experiment are used to determine oligomer structures and what can be done to improve the integration of the two disciplines.

Advances in the Simulation of Protein Aggregation at the Atomistic Scale

Protein aggregation into highly structured amyloid fibrils is associated with various diseases including Alzheimer's disease, Parkinson's disease, and type II diabetes. Amyloids can also have normal biological functions and, in the future, could be used as the basis for novel nanoscale materials. However, a full understanding of the physicochemical forces that drive protein aggregation is still lacking. Such understanding is crucial for the development of drugs that can effectively inhibit aberrant amyloid aggregation and for the directed design of functional amyloids. Atomistic simulations can help understand protein aggregation. In particular, atomistic simulations can be used to study the initial formation of toxic oligomers which are hard to characterize experimentally and to understand the difference in aggregation behavior between different amyloidogenic peptides. Here, we review the latest atomistic simulations of protein aggregation, concentrating on amyloidogenic protein fragments, and provide an outlook for the future in this field.

π-π Stacking Mediated Chirality in Functional Supramolecular Filaments

While a great diversity of peptide-based supra-molecular filaments have been reported, the impact of an auxiliary segment on the chiral assembly of peptides remains poorly understood. Herein we report on the formation of chiral filaments by the self-assembly of a peptide-drug conjugate containing an aromatic drug camptothecin (CPT) in a computational study. We find that the chirality of the filament is mediated by the π‒π stacking between CPTs, not only by the well-expected intermolecular hydrogen bonding between peptide segments. Our simulations show that π‒π stacking of CPTs governs the early stages of the self-assembly process, while a hydrogen bonding network starts at a relatively later stage to contribute to the eventual morphology of the filament. Our results also show the possible presence of water within the core of the CPT filament. These results provide very useful guiding principles for the rational design of supramolecular assemblies of peptide conjugates with aromatic segments.

Advances in free-energy-based simulations of protein folding and ligand binding

Free-energy-based simulations are increasingly providing the narratives about the structures, dynamics and biological mechanisms that constitute the fabric of protein science. Here, we review two recent successes. It is becoming practical: first, to fold small proteins with free-energy methods without knowing substructures and second, to compute ligand-protein binding affinities, not just their binding poses. Over the past 40 years, the timescales that can be simulated by atomistic MD are doubling every 1.3 years--which is faster than Moore's law. Thus, these advances are not simply due to the availability of faster computers. Force fields, solvation models and simulation methodology have kept pace with computing advancements, and are now quite good. At the tip of the spear recently are GPU-based computing, improved fast-solvation methods, continued advances in force fields, and conformational sampling methods that harness external information.

Interplay between the hydrophobic effect and dipole interactions in peptide aggregation at interfaces

Amphipathic octapeptide aggregation at hydrophobic–hydrophilic interfaces is largely driven by backbone dipole interactions in peptide aggregation at interfaces.

New Insights from Sum Frequency Generation Vibrational Spectroscopy into the Interactions of Islet Amyloid Polypeptides with Lipid Membranes

Studies of amyloid polypeptides on membrane surfaces have gained increasing attention in recent years. Several studies have revealed that membranes can catalyze protein aggregation and that the early products of amyloid aggregation can disrupt membrane integrity, increasing water permeability and inducing ion cytotoxicity. Nonetheless, probing aggregation of amyloid proteins on membrane surfaces is challenging. Surface-specific methods are required to discriminate contributions of aggregates at the membrane interface from those in the bulk phase and to characterize protein secondary structures in situ and in real time without the use of perturbing spectroscopic labels. Here, we review the most recent applications of sum frequency generation (SFG) vibrational spectroscopy applied in conjunction with computational modeling techniques, a joint experimental and computational methodology that has provided valuable insights into the aggregation of islet amyloid polypeptide (IAPP) on membrane surfaces. These applications show that SFG can provide detailed information about structures, kinetics, and orientation of IAPP during interfacial aggregation, relevant to the molecular mechanisms of type II diabetes. These recent advances demonstrate the promise of SFG as a new approach for studying amyloid diseases at the molecular level and for the rational drug design targeting early aggregation products on membrane surfaces.

Tau Aggregation Propensity Engrained in Its Solution State

A peptide fragment of the human tau protein which stacks to form neat cross β-sheet fibrils, resembling that found in pathological aggregation, ²⁷³GKVQIINKKLDL²⁸⁴ (here “R2/WT”), was modified with a spin-label at the N-terminus. With the resulting peptide, R2/G273C-SL, we probed events at time scales spanning seconds to hours after aggregation is initiated using transmission electron microscopy (TEM), thioflavin T (THT) fluorescence, ion mobility mass spectrometry (IMMS), electron paramagnetic resonance (EPR), and Overhauser dynamic nuclear polarization (ODNP) to determine if deliberate changes to its conformational states and population in solution influence downstream propensity to form fibrillar aggregates. We find varying solution conditions by adding the osmolyte urea or TMAO, or simply using different buffers (acetate buffer, phosphate buffer, or water), produces significant differences in early monomer/dimer populations and conformations. Crucially, these characteristics of the peptide in solution state before aggregation is initiated dictate the fibril formation propensity after aggregation. We conclude the driving forces that accelerate aggregation, when heparin is added, do not override the subtle intra- or interprotein interactions induced by the initial solvent conditions. In other words, the balance of protein–protein vs protein–solvent interactions present in the initial solution conditions is a critical driving force for fibril formation.

A covalent homodimer probing early oligomers along amyloid aggregation

Early oligomers are crucial in amyloid aggregation; however, due to their transient nature they are among the least structurally characterized species. We focused on the amyloidogenic protein beta2-microglobulin (β2m) whose early oligomers are still a matter of debate. An intermolecular interaction between D strands of facing β2m molecules was repeatedly observed, suggesting that such interface may be relevant for β2m dimerization. In this study, by mutating Ser33 to Cys, and assembling the disulphide-stabilized β2m homodimer (DimC33), such DD strand interface was locked. Although the isolated DimC33 display a stability similar to wt β2m under native conditions, it shows enhanced amyloid aggregation propensity. Three distinct crystal structures of DimC33 suggest that dimerization through the DD interface is instrumental for enhancing DimC33 aggregation propensity. Furthermore, the crystal structure of DimC33 in complex with the amyloid-specific dye Thioflavin-T pinpoints a second interface, which likely participates in the first steps of β2m aggregation. The present data provide new insight into β2m early steps of amyloid aggregation.

Early Events in the Amyloid Formation of the A546T Mutant of Transforming Growth Factor β-Induced Protein in Corneal Dystrophies Compared to the Nonfibrillating R555W and R555Q Mutants

The human transforming growth factor β-induced protein (TGFBIp) is involved in several types of corneal dystrophies where protein aggregation and amyloid fibril formation severely impair vision. Most disease-causing mutations are located in the last of four homologous fasciclin-1 (FAS1) domains of the protein, and it has been shown that when isolated, the fourth FAS1 domain (FAS1-4) mimics the behavior of full-length TGFBIp. In this study, we use molecular dynamics simulations and principal component analysis to study the wild-type FAS1-4 domain along with three disease-causing mutations (R555W, R555Q, and A546T) to decipher any internal difference in dynamical properties of the domains that may explain their varied stabilities and aggregation properties. In addition, we use a protein-protein docking method in combination with chemical cross-linking experiments and mass spectrometry of the cross-linked species to obtain information about interaction faces between identical FAS1-4 domains. The results show that the pathogenic mutations A546T and R555W affect the packing in the hydrophobic core of FAS1-4 in different directions. We further show that the FAS1-4 monomers associate using their β-rich regions, consistent with peptides observed to be part of the amyloid fibril core in lattice corneal dystrophy patients.

Structures of the Alzheimer's Wild-Type Aβ1-40 Dimer from Atomistic Simulations

We have studied the dimer of amyloid beta peptide Aβ of 40 residues by means of all-atom replica exchange molecular dynamics. The Aβ-dimers have been found to be the smallest toxic species in Alzheimer's disease, but their inherent flexibilities have precluded structural characterization by experimental methods. Though the 24-μs-scale simulation reveals a mean secondary structure of 18% β-strand and 10% α helix, we find transient configurations with an unstructured N-terminus and multiple β-hairpins spanning residues 17-21 and 30-36, but the antiparallel and perpendicular peptide orientations are preferred over the parallel organization. Short-lived conformational states also consist of all α topologies, and one compact peptide with β-sheet structure stabilized by a rather extended peptide with α-helical content. Overall, this first all-atom study provides insights into the equilibrium structure of the Aβ1-40 dimer in aqueous solution, opening a new avenue for a comprehensive understanding of the impact of pathogenic and protective mutations in early-stage Alzheimer's disease on a molecular level.

Elucidation of the Aggregation Pathways of Helix-Turn-Helix Peptides: Stabilization at the Turn Region Is Critical for Fibril Formation

Aggregation of proteins to fiberlike aggregates often involves a transformation of native monomers to β-sheet-rich oligomers. This general observation underestimates the importance of α-helical segments in the aggregation cascade. Here, using a combination of experimental techniques and accelerated molecular dynamics simulations, we investigate the aggregation of a 43-residue, apolipoprotein A-I mimetic peptide and its E21Q and D26N mutants. Our study indicates a strong propensity of helical segments not to adopt cross-β-fibrils. The helix-turn-helix monomeric conformation of the peptides is preserved in the mature fibrils. Furthermore, we reveal opposite effects of mutations on and near the turn region in the self-assembly of these peptides. We show that the E21-R24 salt bridge is a major contributor to helix-turn-helix folding, subsequently leading to abundant fibril formation. On the other hand, the K19-D26 interaction is not required to fold the native helix-turn-helix peptide. However, removal of the charged D26 residue decreases the stability of the helix-turn-helix monomer and consequently reduces the level of aggregation. Finally, we provide a more refined assembly model for the helix-turn-helix peptides from apolipoprotein A-I based on the parallel stacking of helix-turn-helix dimers.