Two-step nucleation of amyloid fibrils: omnipresent or not?

Unveiling the Assembly Transition of Diphenylalanine and Its Analogs: from Oligomer Equilibrium to Nanocluster Formation

Peptide self-assembly is fundamental to various biological processes and holds significant potential for nanotechnology and biomedical applications. Despite progress in understanding larger-scale assemblies, the early formation of low-molecular-weight oligomers remains poorly understood. In this study, we investigate the aggregation behavior of the self-assembling diphenylalanine (FF) peptide and its analogs. Utilizing single-nanopore analysis, we detected and characterized the low-molecular-oligomer formation of FF, N-tert-butoxycarbonyl-diphenylalanine (BocFF), fluorenylmethyloxycarbonyl-diphenylalanine (FmocFF), and fluorenylmethyloxycarbonyl-pentafluoro-phenylalanine (Fmoc-F5-Phe) in real time. This approach provided detailed insights into the early stages of peptide self-assembly, revealing the dynamic behavior and formation kinetics of low-molecular-weight oligomeric species. Analysis revealed that the trimer is the key nucleus for FF, while the dimer is the primary nucleus for FmocFF and Fmoc-F5-Phe aggregation, whereas both the dimer and trimer serve as nuclei for BocFF. Mass photometry was employed to track the evolution of these oligomers, revealing the transition from low- to high-molecular-weight species, thereby elucidating intermediate phases in the aggregation process. Transmission electron microscopy and Fourier transform infrared spectroscopy were further employed to characterize the final assembly states, offering high-resolution imaging of morphological structures and detailed information on secondary structures. Based on these analyses, we constructed a comprehensive graph that correlates the entire aggregation processes of the tested self-assembling peptides across multiple scales. This integrative approach provides a holistic understanding of peptide self-assembly, particularly in the formation of low-molecular-weight oligomers toward mature supramolecular structures. These findings shed light on their assembly pathways and structural properties, advancing our understanding of their assembly pathways for nanotechnology and biomedical applications.

Atomic force microscopy of spherical intermediates on the pathway to fibril formation of influenza A virus nuclear export protein

The nuclear export protein of the influenza A virus (NEP) is involved in many important processes of the virus life cycle. This makes it an attractive target for the treatment of a disease caused by a virus. Previously it has been shown, that recombinant variants of NEP are highly prone to aggregation in solution under various conditions with the formation of amyloid-like aggregates. In the present work, the amyloid nature of NEP aggregates was evidenced by Congo red binding assays. Atomic force microscopy has shown that NEP can form two types of spherical nanoparticles, which provide an alternative pathway for the formation of amyloid-like fibrils. Type I of these "fibrillogenic" spheres, formed under physiological conditions, represents the micelle-like particles with height 10-60 nm, which can generate worm-like flexible fibrils with the diameter 2.5-4.0 nm, length 20-500 nm and the Young's modulus ~73 MPa. Type II spherical aggregates with size of about 400-1000 nm, formed at elevated temperatures, includes fractions of drop-like and vesicle-like particles, generating more rigid amyloid-like fibrils with height of ~8 nm, and length of up to 2 μm. The hypothetical mechanism of fibril formation via nanospherical structures was suggested. RESEARCH HIGHLIGHTS: AFM has revealed two types of the influenza A virus nuclear export protein spherical aggregates. They provide an alternative pathway for the formation of amyloid-like fibrils. The mechanism of fibril formation via spherical structures is suggested.

Protein misfolding and amyloid nucleation through liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) is an emerging phenomenon in cell physiology and diseases. The weak multivalent interaction prerequisite for LLPS is believed to be facilitated through intrinsically disordered regions, which are prevalent in neurodegenerative disease-associated proteins. These aggregation-prone proteins also exhibit an inherent property for phase separation, resulting in protein-rich liquid-like droplets. The very high local protein concentration in the water-deficient confined microenvironment not only drives the viscoelastic transition from the liquid to solid-like state but also most often nucleate amyloid fibril formation. Indeed, protein misfolding, oligomerization, and amyloid aggregation are observed to be initiated from the LLPS of various neurodegeneration-related proteins. Moreover, in these cases, neurodegeneration-promoting genetic and environmental factors play a direct role in amyloid aggregation preceded by the phase separation. These cumulative recent observations ignite the possibility of LLPS being a prominent nucleation mechanism associated with aberrant protein aggregation. The present review elaborates on the nucleation mechanism of the amyloid aggregation pathway and the possible early molecular events associated with amyloid-related protein phase separation. It also summarizes the recent advancement in understanding the aberrant phase transition of major proteins contributing to neurodegeneration focusing on the common disease-associated factors. Overall, this review proposes a generic LLPS-mediated multistep nucleation mechanism for amyloid aggregation and its implication in neurodegeneration.

Amyloids, amorphous aggregates and assemblies of peptides - Assessing aggregation

Amyloid and amorphous aggregates represent the two major categories of aggregates associated with diseases, and although exhibiting distinct features, researchers often treat them as equivalent, which demonstrates the need for more thorough characterization. Here, we compare amyloid and amorphous aggregates based on their biochemical properties, kinetics, and morphological features. To further decipher this issue, we propose the use of peptide self-assemblies as minimalistic models for understanding the aggregation process. Peptide building blocks are significantly smaller than proteins that participate in aggregation, however, they make a plausible means to bridge the gap in discerning the aggregation process at the more complex, protein level. Additionally, we explore the potential use of peptide-inspired models to research the liquid-liquid phase separation as a feasible mechanism preceding amyloid formation. Connecting these concepts can help clarify our understanding of aggregation-related disorders and potentially provide novel drug targets to impede and reverse these serious illnesses.

Physicochemical mechanisms of aggregation and fibril formation of α-synuclein and apolipoprotein A-I

Deposition and accumulation of amyloid fibrils is a hallmark of a group of diseases called amyloidosis and neurodegenerative disorders. Although polypeptides potentially have a fibril-forming propensity, native proteins have evolved into proper functional conformations to avoid aggregation and fibril formation. Understanding the mechanism for regulation of fibril formation of native proteins provides clues for the rational design of molecules for inhibiting fibril formation. Although fibril formation is a complex multistep reaction, experimentally obtained fibril formation curves can be fitted with the Finke-Watzky (F-W) two-step model for homogeneous nucleation followed by autocatalytic fibril growth. The resultant F-W rate constants for nucleation and fibril formation provide information on the chemical kinetics of fibril formation. Using the F-W two-step model analysis, we investigated the physicochemical mechanisms of fibril formation of a Parkinson's disease protein α-synuclein (αS) and a systemic amyloidosis protein apolipoprotein A-I (apoA-I). The results indicate that the C-terminal region of αS enthalpically and entropically suppresses nucleation through the intramolecular interaction with the N-terminal region and the intermolecular interaction with existing fibrils. In contrast, the nucleation of the N-terminal fragment of apoA-I is entropically driven likely due to dehydration of large hydrophobic segments in the molecule. Based on our recent findings, we discuss the similarity and difference of the fibril formation mechanisms of αS and the N-terminal fragment of apoA-I from the physicochemical viewpoints.

Multistep molecular mechanisms of Aβ16-22 fibril formation revealed by lattice Monte Carlo simulations

As a model of self-assembly from disordered monomers to fibrils, the amyloid-β fragment Aβ16-22 was subject to past numerous experimental and computational studies. Because dynamics information between milliseconds and seconds cannot be assessed by both studies, we lack a full understanding of its oligomerization. Lattice simulations are particularly well suited to capture pathways to fibrils. In this study, we explored the aggregation of 10 Aβ16-22 peptides using 65 lattice Monte Carlo simulations, each simulation consisting of 3 × 109 steps. Based on a total of 24 and 41 simulations that converge and do not converge to the fibril state, respectively, we are able to reveal the diversity of the pathways leading to fibril structure and the conformational traps slowing down the fibril formation.

Electrostatics-Induced Nucleated Conformational Transition of Protein Aggregation

Despite the wide existence of protein aggregation in nature and its intimate connection to many human diseases, the underlying mechanism remains unclear. Here, we develop a molecular theory by systematically incorporating the self-consistent field theory for charged macromolecules into the dilute solution thermodynamics. The kinetic pathway is tracked without any restriction on the morphology of the aggregates. We find that protein aggregation at low salt concentrations is via a two-step nucleated process involving a conformational transition from metastable spherical oligomer to elongated fibril. The scaling analysis elucidates the electrostatic origin of the conformational transition: the fibril enters the screening region much earlier than the spherical aggregate. As salt concentration increases, the classical mode of one-step nucleation corresponding to macroscopic liquid-liquid phase separation is recovered. Our results reveal that the screened electrostatic interaction is essential for the existence of the metastable oligomer and its subsequent conformational transition to fibril. The theoretical predictions of the kinetic pathway and the morphology of the aggregates are in good agreement with the experimental observations of real proteins.

Amyloid Protein Cross-Seeding Provides a New Perspective on Multiple Diseases In Vivo

Amyloid protein cross-seeding is a peculiar phenomenon of cross-spreading among different diseases. Unlike traditional infectious ones, diseases caused by amyloid protein cross-seeding are spread by misfolded proteins instead of pathogens. As a consequence of the interactions among misfolded heterologous proteins or polypeptides, amyloid protein cross-seeding is considered to be the crucial cause of overlapping pathological transmission between various protein misfolding disorders (PMDs) in multiple tissues and cells. Here, we briefly review the phenomenon of cross-seeding among amyloid proteins. As an interesting example worth mentioning, the potential links between the novel coronavirus pneumonia (COVID-19) and some neurodegenerative diseases might be related to the amyloid protein cross-seeding, thus may cause an undesirable trend in the incidence of PMDs around the world. We then summarize the theoretical models as well as the experimental techniques for studying amyloid protein cross-seeding. Finally, we conclude with an outlook on the challenges and opportunities for basic research in this field. Cross-seeding of amyloid opens up a new perspective in our understanding of the process of amyloidogenesis, which is crucial for the development of new treatments for diseases. It is therefore valuable but still challenging to explore the cross-seeding system of amyloid protein as well as to reveal the structural basis and the intricate processes.

Inhibition of Amyloid Nucleation by Steric Hindrance

Despite recent experiments and simulations suggesting that small-molecule inhibitors and some post-translational modifications (e.g., glycosylation and ubiquitination) can suppress the pathogenic aggregation of proteins due to steric hindrance, the effect of steric hindrance on amyloid formation has not been systematically studied. Based on Monte Carlo simulations using a coarse-grained model for amyloidogenic proteins and a hard sphere acting as steric hindrance, we investigated how steric hindrance on proteins could affect amyloid formation, particularly two steps of primary nucleation, namely, oligomerization and conformational conversion into a β-sheet-enriched nucleus. We found that steric spheres played an inhibitory role in oligomerization with the effect proportional to the sphere radius R_S, which we attributed to the decline in the nonspecific attractions between proteins. During the second step, small steric spheres facilitated the conformational conversion of proteins while large ones suppressed the conversion. The overall steric effect on amyloid nucleation was inhibitory regardless of R_S. As R_S increased, oligomeric assemblies changed from amorphous into sheet-like, structurally ordered species, reminiscent of the structure of amyloid fibrils. The oligomers with large R_S were off-pathway with their ordered structures induced by the competition between steric hindrance and nonspecific attractions of soluble proteins. Interestingly, the equimolar mixture of proteins with and without steric hindrance amplified the sterically inhibitory effect by increasing the energy barrier of protein's conformational conversion. The physical mechanisms and biological implications of the above results are discussed. Our findings improve the current understanding of how nature regulates protein aggregation and amyloid formation by steric hindrance.

Salt-Inducing Assembly Polymorphism Strategy for Cytotoxicity Differentiation of Phenol-Soluble Modulin α3 Assemblies

Phenol-soluble modulin α3 (PSMα3) can self-assemble into fibrous assemblies with a unique "cross-α" sheet structure, which serves as a key virulence factor in the infection of Staphylococcus aureus. However, the structure-cytotoxicity relationships of PSMα3 still remain elusive. Herein, we utilized the strategy of salt-inducing assembly polymorphism to controllably prepare three PSMα3 assemblies with morphological and structural distinctions, including amorphous aggregates (AAs), rigid fibrils (RFs), and oligomers/curvilinear fibrils (OCFs), which provided a convincing method to facilitate the structure-cytotoxicity investigation of PSMα3 assemblies. Our results affirmed that amyloid fibrillation was essential for the enhancement of PSMα3 cytotoxicity, which was proved based on the evidence that RFs and OCFs both triggered more obvious cytotoxicity than AAs. Furthermore, our study also demonstrated that the cytotoxicity was severely dependent on the size and structure of PSMα3 fibrils. In detail, smaller OCFs rich in α-helices exhibited stronger virulence than RFs with larger sizes and low α-helical contents. The cytotoxicity caused by such fibrils was achieved via a membrane-disrupting mechanism, in which RFs and OCFs might be prone to membrane thinning and perforation, respectively. This strategy of salt-inducing PSMα3 assembly polymorphism facilitated the comprehension of the relationship between the characteristics of PSMα3 assemblies and their cytotoxicity and was also helpful to understanding the intrinsic assembly mechanism of the PSMα3.

Multiscale Exploration of Concentration-Dependent Amyloid-β(16-21) Amyloid Nucleation

Atomic descriptions of peptide aggregation nucleation remain lacking due to the difficulty of exploring complex configurational spaces on long time scales. To elucidate this process, we develop a multiscale approach combining a metadynamics-based method with cluster statistical mechanics to derive concentration-dependent free energy surfaces of nucleation at near-atomic resolution. A kinetic transition network of nucleation is then constructed and employed to systematically explore nucleation pathways and kinetics through stochastic simulations. This approach is applied to describe Aβ_16-21 amyloid nucleation, revealing a two-step mechanism involving disordered aggregates at millimolar concentration, and an unexpected mechanism at submillimolar concentrations that exhibits kinetics reminiscent of classical nucleation but atypical pathways involving growing clusters with structured cores wrapped by disordered surface. When this atypical mechanism is operative, critical nucleus size can be reflected by the nucleation reaction order. Collectively, our approach paves the way for a more quantitative and detailed understanding of peptide aggregation nucleation.

The Ambiguous Functions of the Precursors That Enable Nonclassical Modes of Olanzapine Nucleation and Growth

One of the most consequential assumptions of the classical theories of crystal nucleation and growth is the Szilard postulate, which states that molecules from a supersaturated phase join a nucleus or a growing crystal individually. In the last 20 years, observations in complex biological, geological, and engineered environments have brought to light violations of the Szilard rule, whereby molecules assemble into ordered or disordered precursors that then host and promote nucleation or contribute to fast crystal growth. Nonclassical crystallization has risen to a default mode presumed to operate in the majority of the inspected crystallizing systems. In some cases, the existence of precursors in the growth media is admitted as proof for their role in nucleation and growth. With the example of olanzapine, a marketed drug for schizophrenia and bipolar disorder, we demonstrate that molecular assemblies in the solution selectively participate in crystal nucleation and growth. In aqueous and organic solutions, olanzapine assembles into both mesoscopic solute-rich clusters and dimers. The clusters facilitate nucleation of crystals and crystal form transformations. During growth, however, the clusters land on the crystal surface and transform into defects, but do not support step growth. The dimers are present at low concentrations in the supersaturated solution, yet the crystals grow by the association of dimers, and not of the majority monomers. The observations with olanzapine emphasize that detailed studies of the crystal and solution structures and the dynamics of molecular association may empower classical and nonclassical models that advance the understanding of natural crystallization, and support the design and manufacture of promising functional materials.

Multiscale Models for Fibril Formation: Rare Events Methods, Microkinetic Models, and Population Balances

Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.

Amyloid Oligomers: A Joint Experimental/Computational Perspective on Alzheimer's Disease, Parkinson's Disease, Type II Diabetes, and Amyotrophic Lateral Sclerosis

Protein misfolding and aggregation is observed in many amyloidogenic diseases affecting either the central nervous system or a variety of peripheral tissues. Structural and dynamic characterization of all species along the pathways from monomers to fibrils is challenging by experimental and computational means because they involve intrinsically disordered proteins in most diseases. Yet understanding how amyloid species become toxic is the challenge in developing a treatment for these diseases. Here we review what computer, in vitro, in vivo, and pharmacological experiments tell us about the accumulation and deposition of the oligomers of the (Aβ, tau), α-synuclein, IAPP, and superoxide dismutase 1 proteins, which have been the mainstream concept underlying Alzheimer's disease (AD), Parkinson's disease (PD), type II diabetes (T2D), and amyotrophic lateral sclerosis (ALS) research, respectively, for many years.

Chemical control of peptide material phase transitions

Progressive solute-rich polymer phase transitions provide pathways for achieving ordered supramolecular assemblies. Intrinsically disordered protein domains specifically regulate information in biological networks via conformational ordering. Here we consider a molecular tagging strategy to control ordering transitions in polymeric materials and provide a proof-of-principle minimal peptide phase network captured with a dynamic chemical network.

Substrate initiated assembly of a dynamic chemical network.

Amyloids and their untapped potential as hydrogelators

Amyloid fibrils are cross-β-sheet-rich fibrous aggregates. They were originally identified as disease-associated protein/peptide deposits. The cross-β motif was consequently labelled as an alien and pathogenic fold. Subsequent research revealed that the fibrillar aggregates were benign, and the cytotoxicity in the amyloid diseases was attributed to the pre-fibrillar structures. Research in the past two decades has identified the native functional amyloids in organisms ranging from bacteria to human. The amyloid-like fibrils, therefore, are not necessarily pathogenic, and the cross-β motif is very much native. This premise makes way for the amyloids to be used as biocompatible materials. Many naturally occurring amyloidogenic proteins/peptides or their fragments have been reported in the literature to form hydrogels. Hydrogels constitute one of the most interesting classes of soft materials that find application in diverse fields such as environmental, electronic, and biomedical engineering. Applications of hydrogels in medicine are particularly extensive. Among various classes of peptides that form hydrogels, the potential of amyloids is largely untapped. In this review, we have attempted to compile the literature on amyloid hydrogels and discuss their potential applications.

Clustering and Fibril Formation during GNNQQNY Aggregation: A Molecular Dynamics Study

The precise kinetic pathways of peptide clustering and fibril formation are not fully understood. Here we study the initial clustering kinetics and transient cluster morphologies during aggregation of the heptapeptide fragment GNNQQNY from the yeast prion protein Sup35. We use a mid-resolution coarse-grained molecular dynamics model of Bereau and Deserno to explore the aggregation pathways from the initial random distribution of free monomers to the formation of large clusters. By increasing the system size to 72 peptides we could follow directly the molecular events leading to the formation of stable fibril-like structures. To quantify those structures we developed a new cluster helicity parameter. We found that the formation of fibril-like structures is a cooperative processes that requires a critical number of monomers, M⋆≈25, in a cluster. The terminal tyrosine residue is the structural determinant in the formation of helical fibril-like structures. This work supports and quantifies the two-step aggregation model where the initially formed amorphous clusters grow and, when they are large enough, rearrange into mature twisted structures. However, in addition to the nucleated fibrillation, growing aggregates undergo further internal reorganization, which leads to more compact structures of large aggregates.

A two-step biopolymer nucleation model shows a nonequilibrium critical point

Biopolymer self-assembly pathways are complicated by the ability of their monomeric subunits to adopt different conformational states. This means nucleation often involves a two-step mechanism where the monomers first condense to form a metastable intermediate, which then converts to a stable polymer by conformational rearrangement of constituent monomers. Nucleation intermediates play a causative role in amyloid diseases such as Alzheimer's and Parkinson's. While existing mathematical models neglect the conversion dynamics, experiments show that conversion events frequently occur on comparable timescales to the condensation of intermediates and growth of mature polymers and thus cannot be ignored. We present a model that explicitly accounts for simultaneous assembly and conversion. To describe conversion, we propose an experimentally motivated initiation-propagation mechanism in which the stable phase arises locally within the intermediate and then spreads by nearest-neighbor interactions, in a manner analogous to one-dimensional Glauber dynamics. Our analysis shows that the competing timescales of assembly and conversion result in a nonequilibrium critical point, separating a regime where intermediates are kinetically unstable from one where conformationally mixed intermediates accumulate. This strongly affects the accumulation rate of the stable biopolymer phase. Our model is uniquely able to explain experimental phenomena such as the formation of mixed intermediates and abrupt changes in the scaling exponent γ, which relates the total monomer concentration to the accumulation rate of the stable phase. This provides a first step toward a general model of two-step biopolymer nucleation, which can quantitatively predict the concentration and composition of biologically crucial intermediates.

Thermodynamics of Huntingtin Aggregation

Amyloid aggregates are found in many neurodegenerative diseases, including Huntington's, Alzheimer's, and prion diseases. The precise role of the aggregates in disease progression has been difficult to elucidate because of the diversity of aggregated states they can adopt. Here, we study the formation of fibrils and oligomers by exon 1 of huntingtin protein. We show that the oligomer states are consistent with polymer micelles that are limited in size by the stretching entropy of the polyglutamine region. The model shows how the sequences flanking the amyloid core modulate aggregation behavior. The N17 region promotes aggregation through weakly attractive interactions, whereas the C38 tail opposes aggregation via steric repulsion. We also show that the energetics of cross-β stacking by polyglutamine would produce fibrils with many alignment defects, but minor perturbations from the flanking sequences are sufficient to reduce the defects to the level observed in experiment. We conclude with a discussion of the implications of this model for other amyloid-forming molecules.

Aggregation kinetics of short peptides: All-atom and coarse-grained molecular dynamics study

Peptides can aggregate into ordered structures with different morphologies. The aggregation mechanism and evolving structures are the subject of intense research. In this paper we have used molecular dynamics to examine the sequence-dependence of aggregation kinetics for three short peptides: octaalanine (Ala8), octaasparagine (Asn8), and the heptapeptide GNNQQNY (abbreviated as GNN). First, we compared the aggregation of 20 randomly distributed peptides using the coarse-grained MARTINI force field and the atomistic OPLS-AA force field. We found that the MARTINI and OPLS-AA aggregation kinetics are similar for Ala8, Asn8, and GNN. Second, we used the MARTINI force field to study the early stages of aggregation kinetics for a larger system with 72 peptides. In the initial stage of aggregation small clusters grow by monomer addition. In the second stage, when the free monomers are depleted, the dominant cluster growth path is cluster-cluster coalescence. We quantified the aggregation kinetics in terms of rate equations. Our study shows that the initial aggregation kinetics are similar for Ala8, Asn8, and GNN but the molecular details can be different, especially for MARTINI Ala8. We hypothesize that peptide aggregation proceed in two steps. In the first step amorphous aggregates are formed, and then, in the second step, they reorganize into ordered structures. We conclude that sequence-specific differences show up in the second step of aggregation.

Aggregation behavior of the amyloid model peptide NACore

The aggregation of the 11 residue long NACore peptide segment of α-synuclein (68-GAVVTGVTAVA-78) has been investigated using a combination of cryogenic transmission electron microscopy (cryo-TEM), small- and wide-angle X-ray scattering, and spectroscopy techniques. The aqueous peptide solubility is pH dependent, and aggregation was triggered by a pH quench from pH 11.3 to approximately pH 8 or 6, where the average peptide net charge is weakly negative (pH 8), or essentially zero (pH 6). Cryo-TEM shows the presence of long and stiff fibrillar aggregates at both pH, that are built up from β-sheets, as demonstrated by circular dichroism spectroscopy and thioflavin T fluorescence. The fibrils are crystalline, with a wide angle X-ray diffraction pattern that is consistent with a previously determined crystal structure of NACore. Of particular note is the cryo-TEM observation of small globular shaped aggregates, of the order of a few nanometers in size, adsorbed onto the surface of already formed fibrils at pH 6. The fibrillation kinetics is slow, and occurs on the time scale of days. Similarly slow kinetics is observed at both pH, but slightly slower at pH 6, even though the peptide solubility is here expected to be lower. The observation of the small globular shaped aggregates, together with the associated kinetics, could be highly relevant in relation to mechanisms of secondary nucleation and oligomer formation in amyloid systems.

Multiscale Aggregation of the Amyloid Aβ16-22 Peptide: From Disordered Coagulation and Lateral Branching to Amorphous Prefibrils

In this work we investigate the multiscale dynamics of the aggregation process of an amyloid peptide, Aβ_16-22. By performing massive coarse-grained simulations at the quasi-atomistic resolution and including hydrodynamic effects, we followed the formation and growth of a large elongated aggregate and its slow structuring. The elongation proceeds via a two-step nucleation mechanism with disordered aggregates formed initially and subsequently fusing to elongate the amorphous prefibril. A variety of coagulation events coexist, including lateral growth. The latter mechanism, sustained by long-range hydrodynamics correlations, actually can create a large branched structure spanning a few tens of nanometers. Our findings confirm the experimental hypothesis of a critical contribution of lateral growth to the amyloid aggregation kinetics and the capability of our model to sample critical structures like prefibril hosting annular pores.

Unified theoretical description of the kinetics of protein aggregation

Solution conditions chosen for the production of amyloid can also promote formation of significant extents of amorphous protein aggregate. In one interpretation, the amyloid and amorphous aggregation pathways are considered to be in competition with each other. An alternative conceptualization involves considering amorphous aggregation as an obligatory intermediate process of the amyloid formation pathway. Here, we review recently developed macroscopic-level theories of protein aggregation that unify these two competing models into a single paradigm. Key features of the unified model included (1) a description of the amorphous aggregate as a second liquid phase with the degree of liquid-like character determined by the mobility of the monomer within it, and (2) heterogeneous growth pathways based on nucleation, growth, and fragmentation of amyloid occurring within different phases and at their interfacial boundary. Limiting-case behaviors of the protein aggregation reaction, either singly involving amyloid or amorphous aggregate production, and mixed-case behaviors, involving competitive and/or facilitated growth of amorphous and amyloid species, are presented and reviewed in context. This review principally describes an approach developed by Hirota and Hall 2019 (Hirota, N. and Hall, D. 2019. Protein Aggregation Kinetics: A Unified Theoretical Description. Chapter 7 of 'Protein Solubility and Amorphous Aggregation: From Academic Research to Applications in Drug Discovery and Bioindustry' edited by Y. Kuroda and F. Arisaka. CMC Publishers). Sections of that work are translated from the original Japanese and republished here with the full permission of CMC Publishing Corporation.

Obstacles to translating the promise of nanoparticles into viable amyloid disease therapeutics

Nanoparticles (NPs) constitute a powerful therapeutic platform with exciting prospects as potential inhibitors of amyloid-[Formula: see text] (Aβ) aggregation, a process associated with Alzheimer's disease (AD). Researchers have synthesized and tested a large collection of NPs with disparate sizes, shapes, electrostatic properties and surface ligands that evoke a variety of responses on Aβ aggregation. In spite of a decade of research on the NP-Aβ system and many promising experimental results, NPs have failed to progress to any level of clinical trials for AD. A theoretical framework with which to approach this physical system is presented featuring two simple metrics, (1) the extent to which NPs adsorb Aβ, and (2) the degree to which interaction with a NP alters Aβ conformation relative to aggregation propensity. Most of our current understanding of these two interactions has been gained through experimentation, and many of these studies are reviewed herein. We also provide a potential roadmap for studies that we believe could produce viable NPs as an effective AD therapeutic platform.

Anomalous Dense Liquid Condensates Host the Nucleation of Tumor Suppressor p53 Fibrils

About half of human cancers are associated with mutations of the tumor suppressor p53. Gained oncogenic functions of the mutants have been related to aggregation behaviors of wild-type and mutant p53. The thermodynamic and kinetic mechanisms of p53 aggregation are poorly understood. Here we find that wild-type p53 forms an anomalous liquid phase. The liquid condensates exhibit several behaviors beyond the scope of classical phase transition theories: their size, ca. 100 nm, is independent of the p53 concentration and decoupled from the protein mass held in the liquid phase. Furthermore, the liquid phase lacks constant solubility. The nucleation of p53 fibrils deviates from the accepted mechanism of sequential association of single solute molecules. We find that the liquid condensates serve as pre-assembled precursors of high p53 concentration that facilitate fibril assembly. Fibril nucleation hosted by precursors represents a novel biological pathway, which opens avenues to suppress protein fibrillation in aggregation diseases.

Biomolecular Assemblies: Moving from Observation to Predictive Design

Biomolecular assembly is a key driving force in nearly all life processes, providing structure, information storage, and communication within cells and at the whole organism level. These assembly processes rely on precise interactions between functional groups on nucleic acids, proteins, carbohydrates, and small molecules, and can be fine-tuned to span a range of time, length, and complexity scales. Recognizing the power of these motifs, researchers have sought to emulate and engineer biomolecular assemblies in the laboratory, with goals ranging from modulating cellular function to the creation of new polymeric materials. In most cases, engineering efforts are inspired or informed by understanding the structure and properties of naturally occurring assemblies, which has in turn fueled the development of predictive models that enable computational design of novel assemblies. This Review will focus on selected examples of protein assemblies, highlighting the story arc from initial discovery of an assembly, through initial engineering attempts, toward the ultimate goal of predictive design. The aim of this Review is to highlight areas where significant progress has been made, as well as to outline remaining challenges, as solving these challenges will be the key that unlocks the full power of biomolecules for advances in technology and medicine.

Mechanisms and rates of nucleation of amyloid fibrils

The classical nucleation theory finds the rate of nucleation proportional to the monomer concentration raised to the power, which is the "critical nucleus size," n_c. The implicit assumption, that amyloids nucleate in the same way, has been recently challenged by an alternative two-step mechanism, when the soluble monomers first form a metastable aggregate (micelle) and then undergo conversion into the conformation rich in β-strands that are able to form a stable growing nucleus for the protofilament. Here we put together the elements of extensive knowledge about aggregation and nucleation kinetics, using a specific case of Aβ_1-42 amyloidogenic peptide for illustration, to find theoretical expressions for the effective rate of amyloid nucleation. We find that at low monomer concentrations in solution and also at low interaction energy between two peptide conformations in the micelle, the nucleation occurs via the classical route. At higher monomer concentrations, and a range of other interaction parameters between peptides, the two-step "aggregation-conversion" mechanism of nucleation takes over. In this regime, the effective rate of the process can be interpreted as a power of monomer concentration in a certain range of parameters; however, the exponent is determined by a complicated interplay of interaction parameters and is not related to the minimum size of the growing nucleus (which we find to be ∼7-8 for Aβ_1-42).

Impact of membrane curvature on amyloid aggregation

The misfolding, amyloid aggregation, and fibril formation of intrinsically disordered proteins/peptides (or amyloid proteins) have been shown to cause a number of disorders. The underlying mechanisms of amyloid fibrillation and structural properties of amyloidogenic precursors, intermediates, and amyloid fibrils have been elucidated in detail; however, in-depth examinations on physiologically relevant contributing factors that induce amyloidogenesis and lead to cell death remain challenging. A large number of studies have attempted to characterize the roles of biomembranes on protein aggregation and membrane-mediated cell death by designing various membrane components, such as gangliosides, cholesterol, and other lipid compositions, and by using various membrane mimetics, including liposomes, bicelles, and different types of lipid-nanodiscs. We herein review the dynamic effects of membrane curvature on amyloid generation and the inhibition of amyloidogenic proteins and peptides, and also discuss how amyloid formation affects membrane curvature and integrity, which are key for understanding relationships with cell death. Small unilamellar vesicles with high curvature and large unilamellar vesicles with low curvature have been demonstrated to exhibit different capabilities to induce the nucleation, amyloid formation, and inhibition of amyloid-β peptides and α-synuclein. Polymorphic amyloidogenesis in small unilamellar vesicles was revealed and may be viewed as one of the generic properties of interprotein interaction-dominated amyloid formation. Several mechanical models and phase diagrams are comprehensively shown to better explain experimental findings. The negative membrane curvature-mediated mechanisms responsible for the toxicity of pancreatic β cells by the amyloid aggregation of human islet amyloid polypeptide (IAPP) and binding of the precursors of the semen-derived enhancer of viral infection (SEVI) are also described. The curvature-dependent binding modes of several types of islet amyloid polypeptides with high-resolution NMR structures are also discussed.

Recent progress on understanding the mechanisms of amyloid nucleation

Amyloid fibrils are supramolecular protein assemblies with a fibrous morphology and cross-β structure. The formation of amyloid fibrils typically follows a nucleation-dependent polymerization mechanism, in which a one-step nucleation scheme has widely been accepted. However, a variety of oligomers have been identified in early stages of fibrillation, and a nucleated conformational conversion (NCC) mechanism, in which oligomers serve as a precursor of amyloid nucleation and convert to amyloid nuclei, has been proposed. This development has raised the need to consider more complicated multi-step nucleation processes in addition to the simplest one-step process, and evidence for the direct involvement of oligomers as nucleation precursors has been obtained both experimentally and theoretically. Interestingly, the NCC mechanism has some analogy with the two-step nucleation mechanism proposed for inorganic and organic crystals and protein crystals, although a more dramatic conformational conversion of proteins should be considered in amyloid nucleation. Clarifying the properties of the nucleation precursors of amyloid fibrils in detail, in comparison with those of crystals, will allow a better understanding of the nucleation of amyloid fibrils and pave the way to develop techniques to regulate it.

Thermodynamic properties of amyloid fibrils in equilibrium

In this manuscript we use a two-dimensional coarse-grained model to study how amyloid fibrils grow towards an equilibrium state where they coexist with proteins dissolved in a solution. Free-energies to dissociate proteins from fibrils are estimated from the residual concentration of dissolved proteins. Consistent with experiments, the concentration of proteins in solution affects the growth rate of fibrils but not their equilibrium state. Also, studies of the temperature dependence of the equilibrium state can be used to estimate thermodynamic quantities, e.g., heat capacity and entropy.

Multistep Conformation Selection in Amyloid Assembly

Defining pathways for amyloid assembly could impact therapeutic strategies for as many as 50 disease states. Here we show that amyloid assembly is subject to different forces regulating nucleation and propagation steps and provide evidence that the more global β-sheet/β-sheet facial complementarity is a critical determinant for amyloid nucleation and structural selection.

Theory of amyloid fibril nucleation from folded proteins

We present a theoretical model for the nucleation of amyloid fibrils. In our model we use helix-coil theory to describe the equilibrium between a soluble native state and an aggregation-prone unfolded state. We then extend the theory to include oligomers with β-sheet cores and calculate the free energy of these states using estimates for the energies of H-bonds, steric zipper interactions, and the conformational entropy cost of forming secondary structure. We find that states with fewer than ~10 β-strands are unstable relative to the dissociated state and three β-strands is the highest free energy state. We then use a modified version of Classical Nucleation Theory to compute the nucleation rate of fibrils from a supersaturated solution of monomers, dimers, and trimers. The nucleation rate has a non-monotonic dependence on denaturant concentration reflecting the competing effects of destabilizing the fibril and increasing the concentration of unfolded monomers. We estimate heterogeneous nucleation rates and discuss the application of our model to secondary nucleation.

Physical principles of filamentous protein self-assembly kinetics

The polymerization of proteins and peptides into filamentous supramolecular structures is an elementary form of self-organization of key importance to the functioning biological systems, as in the case of actin biofilaments that compose the cellular cytoskeleton. Aberrant filamentous protein self-assembly, however, is associated with undesired effects and severe clinical disorders, such as Alzheimer's and Parkinson's diseases, which, at the molecular level, are associated with the formation of certain forms of filamentous protein aggregates known as amyloids. Moreover, due to their unique physicochemical properties, protein filaments are finding extensive applications as biomaterials for nanotechnology. With all these different factors at play, the field of filamentous protein self-assembly has experienced tremendous activity in recent years. A key question in this area has been to elucidate the microscopic mechanisms through which filamentous aggregates emerge from dispersed proteins with the goal of uncovering the underlying physical principles. With the latest developments in the mathematical modeling of protein aggregation kinetics as well as the improvement of the available experimental techniques it is now possible to tackle many of these complex systems and carry out detailed analyses of the underlying microscopic steps involved in protein filament formation. In this paper, we review some classical and modern kinetic theories of protein filament formation, highlighting their use as a general strategy for quantifying the molecular-level mechanisms and transition states involved in these processes.

Brazilin Inhibits Prostatic Acidic Phosphatase Fibrillogenesis and Decreases its Cytotoxicity

A 39-amino acid peptide fragment that is derived from prostatic acidic phosphatase (PAP), PAP_248-286 , is secreted in large amounts in human semen and forms amyloid fibrils. These fibrils can capture HIV virions and increase the attachment of virions to target cells; as such, they are called a "semen-derived enhancer of virus infection" (SEVI). Therefore, the inhibition of the formation of PAP_248-286 amyloid fibrils is of great significance. Herein, we demonstrate that brazilin effectively inhibits PAP_248-286 aggregation. The inhibitory effect increases with increasing brazilin concentration. Thioflavin T fluorescence assays and TEM observations confirmed that a few fibrils formed when brazilin was present with PAP_248-286 in an equimolar concentration. Circular dichroism spectroscopy indicated that brazilin inhibited the secondary structural transitions from α-helices and random coils into β-sheets. Cytotoxicity assays showed that brazilin significantly decreased the cytotoxicity of the fibrils at 0.01 mmol L^-1 . Isothermal titration calorimetry revealed that hydrophobic interactions were the main driving force for the binding of brazilin to the PAP_248-286 monomer (dissociation constant, 4.03 μmol L^-1 ), and that the binding affinity of brazilin for the fibrils was at least three orders of magnitude lower than that for the monomer. These results indicate that brazilin holds great potential as a small-molecule agent against SEVIs.

Two-Dimensional Nucleation on the Terrace of Colloidal Crystals with Added Polymers

Understanding nucleation dynamics is important both fundamentally and technologically in materials science and other scientific fields. Two-dimensional (2D) nucleation is the predominant growth mechanism in colloidal crystallization, in which the particle interaction is attractive, and has recently been regarded as a promising method to fabricate varieties of complex nanostructures possessing innovative functionality. Here, polymers are added to a colloidal suspension to generate a depletion attractive force, and the detailed 2D nucleation process on the terrace of the colloidal crystals is investigated. In the system, we first measured the nucleation rate at various area fractions of particles on the terrace, ϕ_area. In situ observations at single-particle resolution revealed that nucleation behavior follows the framework of classical nucleation theory (CNT), such as single-step nucleation pathway and existence of critical size. Characteristic nucleation behavior is observed in that the nucleation and growth stage are clearly differentiated. When many nuclei form in a small area of the terrace, a high density of kink sites of once formed islands makes growth more likely to occur than further nucleation because nucleation has a higher energy barrier than growth. The steady-state homogeneous 2D nucleation rate, J, and the critical size of nuclei, r*, are measured by in situ observations based on the CNT, which enable us to obtain the step free energy, γ, which is an important parameter for characterizing the nucleation process. The γ value is found to change according to the strength of attraction, which is tuned by the concentration of the polymer as a depletant.

The Impact of Mathematical Modeling in Understanding the Mechanisms Underlying Neurodegeneration: Evolving Dimensions and Future Directions

Neurodegenerative diseases are a heterogeneous group of disorders that are characterized by the progressive dysfunction and loss of neurons. Here, we distil and discuss the current state of modeling in the area of neurodegeneration, and objectively compare the gaps between existing clinical knowledge and the mechanistic understanding of the major pathological processes implicated in neurodegenerative disorders. We also discuss new directions in the field of neurodegeneration that hold potential for furthering therapeutic interventions and strategies.

Kinetic Pathways and Mechanisms of Two-Step Nucleation in Crystallization

Crystallizations often pass through multiple intermediate structures before reaching the final state, such as amorphous precursors, polymorphs, or denser liquid droplets. However, the atomistic pathways from these metastable phases to final crystals still remain unclear. Here, we investigated the structure evolution process from liquid to final crystals of homogeneous nucleation by atomic-scale simulations and analyzed the intrinsic mechanisms that influence the nucleation pathways. Three different pathways of two-step nucleation were found by visualizing the precursors' evolutions, and some new micromechanisms of two-step nucleation are revealed. We suggest that the solid bond fluctuations can trigger the formation of intermediate precursors, while the precursors' packing density dominates the structural transformation pathways from intermediate phases to crystals. These findings not only shed light on the mechanisms of nucleation but also provide guidance for future refinements of two-step nucleation theory.

Nanoscale Structure and Spectroscopic Probing of Aβ1-40 Fibril Bundle Formation

Amyloid plaques composed of fibrillar Amyloid-β (Aβ) are hallmarks of Alzheimer's disease. However, Aβ fibrils are morphologically heterogeneous. Conformation sensitive luminescent conjugated oligothiophenes (LCOs) are versatile tools for monitoring such fibril polymorphism in vivo and in vitro. Biophysical methods applied on in vitro generated Aβ fibrils, stained with LCOs with different binding and fluorescence properties, can be used to characterize the Aβ fibrillation in depth, far beyond that possible for in vivo generated amyloid plaques. In this study, in vitro fibrillation of the Aβ1-40 peptide was monitored by time-lapse transmission electron microscopy, LCO fluorescence, and atomic force microscopy. Differences in the LCO binding in combination with nanoscale imaging revealed that spectral variation correlated with fibrils transforming from solitary filaments (Ø~2.5 nm) into higher order bundled structures (Ø~5 nm). These detailed in vitro experiments can be used to derive data that reflects the heterogeneity of in vivo generated Aβ plaques observed by LCO fluorescence. Our work provides new structural basis for targeted drug design and molecular probe development for amyloid imaging.

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*.