An imaging and systems modeling approach to fibril breakage enables prediction of amyloid behavior

Trace_y: Software algorithms for structural analysis of individual helical filaments by three-dimensional contact point reconstruction atomic force microscopy

Atomic force microscopy (AFM) is a powerful and increasingly accessible technology that has a wide range of bio-imaging applications. AFM is capable of producing detailed three-dimensional topographical images with high signal-to-noise ratio, which enables the structural features of individual molecules to be studied without the need for ensemble averaging. Here, a software tool Trace_y, designed to reconstruct the three-dimensional surface envelopes of individual helical filament structures from topographical AFM images, is presented. Workflow using Trace_y is demonstrated on the structural analysis of individual helical amyloid protein fibrils where the assembly mechanism of heterogeneous, complex and diverse fibril populations due to structural polymorphism is not understood. The algorithms presented here allow structural information encoded in topographical AFM height images to be extracted and understood as three-dimensional (3D) contact point clouds. This approach will facilitate the use of AFM in structural biology to understand molecular structures and behaviors at individual molecule level.

Deciphering the Seed Size-Dependent Cellular Internalization Mechanism for α-Synuclein Fibrils

Aggregation of α-synuclein (α-Syn) and Lewy body (LB) formation are the key pathological events implicated in Parkinson's disease (PD) that spread in a prion-like manner. However, biophysical and structural characteristics of toxic α-Syn species and molecular events that drive early events in the propagation of α-Syn amyloids in a prion-like manner remain elusive. We used a neuronal cell model to demonstrate the size-dependent native biological activities of α-Syn fibril seeds. Biophysical characterization of the fibril seeds generated by controlled fragmentation indicated that increased fragmentation leads to a reduction in fibril size, correlating directly with the extent of fragmentation events. Although the size-based complexity of amyloid fibrils modulates their biological activities and fibril amplification pathways, it remains unclear how the variability of fibril seed size dictates its specific uptake mechanism into the cells. The present study elucidates the mechanism of α-Syn fibril internalization and how it is regulated by the size of fibril seeds. Further, we demonstrate that size-dependent endocytic pathways (dynamin-dependent clathrin/caveolin-mediated) are more prominent for the differential uptake of short fibril seeds compared to their longer counterparts. This size-dependent preference might contribute to the enhanced uptake and transcellular propagation of short α-Syn fibril seeds in a prion-like manner. Overall, the present study suggests that the physical dimension of α-Syn amyloid fibril seeds significantly influences their cellular uptake and pathological responses in the initiation and progression of PD.

Atomic force microscopy 3D structural reconstruction of individual particles in the study of amyloid protein assemblies

Recent developments in atomic force microscopy (AFM) image analysis have made three-dimensional (3D) structural reconstruction of individual particles observed on 2D AFM height images a reality. Here, we review the emerging contact point reconstruction AFM (CPR-AFM) methodology and its application in 3D reconstruction of individual helical amyloid filaments in the context of the challenges presented by the structural analysis of highly polymorphous and heterogeneous amyloid protein structures. How individual particle-level structural analysis can contribute to resolving the amyloid polymorph structure-function relationships, the environmental triggers leading to protein misfolding and aggregation into amyloid species, the influences by the conditions or minor fluctuations in the initial monomeric protein structure on the speed of amyloid fibril formation, and the extent of the different types of amyloid species that can be formed, are discussed. Future perspectives in the capabilities of AFM-based 3D structural reconstruction methodology exploiting synergies with other recent AFM technology advances are also discussed to highlight the potential of AFM as an emergent general, accessible and multimodal structural biology tool for the analysis of individual biomolecules.

Effects of N-terminal Acetylation on the Aggregation of Disease-related α-synuclein Variants

Mutations in the SNCA gene, which encodes the protein α-synuclein, have been linked with early onset Parkinson's disease. The exact nature of this association, however, is still poorly understood. To investigate this problem, we started from the observation that α-synuclein is constitutively N-terminally acetylated, a post-translational modification that alters the charge and structure of α-synuclein molecules and affects their interaction with lipid membranes, as well as their aggregation process. We thus studied five N-terminal acetylated familial variants (A30P, E46K, H50Q, G51D and A53T) of α-synuclein through a wide range of biophysical assays to probe the microscopic steps in their aggregation process and the structures of the resulting aggregates. Our results reveal a great complexity in the combined effects of the disease-related mutations with N-terminal acetylation on the aggregation of α-synuclein, which underscores the great sensitivity to even relatively small perturbations of the behaviour of this protein.

Comparative Analysis of the Relative Fragmentation Stabilities of Polymorphic Alpha-Synuclein Amyloid Fibrils

The division of amyloid fibril particles through fragmentation is implicated in the progression of human neurodegenerative disorders such as Parkinson's disease. Fragmentation of amyloid fibrils plays a crucial role in the propagation of the amyloid state encoded in their three-dimensional structures and may have an important role in the spreading of potentially pathological properties and phenotypes in amyloid-associated diseases. However, despite the mechanistic importance of fibril fragmentation, the relative stabilities of different types or different polymorphs of amyloid fibrils toward fragmentation remain to be quantified. We have previously developed an approach to compare the relative stabilities of different types of amyloid fibrils toward fragmentation. In this study, we show that controlled sonication, a widely used method of mechanical perturbation for amyloid seed generation, can be used as a form of mechanical perturbation for rapid comparative assessment of the relative fragmentation stabilities of different amyloid fibril structures. This approach is applied to assess the relative fragmentation stabilities of amyloid formed in vitro from wild type (WT) α-synuclein and two familial mutant variants of α-synuclein (A30P and A53T) that generate morphologically different fibril structures. Our results demonstrate that the fibril fragmentation stabilities of these different α-synuclein fibril polymorphs are all highly length dependent but distinct, with both A30P and A53T α-synuclein fibrils displaying increased resistance towards sonication-induced fibril fragmentation compared with WT α-synuclein fibrils. These conclusions show that fragmentation stabilities of different amyloid fibril polymorph structures can be diverse and suggest that the approach we report here will be useful in comparing the relative stabilities of amyloid fibril types or fibril polymorphs toward fragmentation under different biological conditions.

Amyloid particles facilitate surface-catalyzed cross-seeding by acting as promiscuous nanoparticles

Amyloid seeds are nanometer-sized protein particles that accelerate amyloid assembly as well as propagate and transmit the amyloid protein conformation associated with a wide range of protein misfolding diseases. However, seeded amyloid growth through templated elongation at fibril ends cannot explain the full range of molecular behaviors observed during cross-seeded formation of amyloid by heterologous seeds. Here, we demonstrate that amyloid seeds can accelerate amyloid formation via a surface catalysis mechanism without propagating the specific amyloid conformation associated with the seeds. This type of seeding mechanism is demonstrated through quantitative characterization of the cross-seeded assembly reactions involving two nonhomologous and unrelated proteins: the human Aβ42 peptide and the yeast prion-forming protein Sup35NM. Our results demonstrate experimental approaches to differentiate seeding by templated elongation from nontemplated amyloid seeding and rationalize the molecular mechanism of the cross-seeding phenomenon as a manifestation of the aberrant surface activities presented by amyloid seeds as nanoparticles.

Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation

The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of ‘pure fragmentation’. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time-dependent experimental measurements of filament size distribution. The numerical approach to systematically analyze the behaviour of pure fragmentation trajectories was also developed. We illustrate how these formulae can be used, provide some insights on their robustness, and show how they inform the design of experiments to measure fibril fragmentation dynamics. These advances are made possible by our central theoretical result on how the length distribution profile of the solution to the pure fragmentation equation aligns with a steady distribution profile for large times.

Amyloid fibrils are fibrillar protein structures involved in many neurodegenerative illnesses, such as Parkinson’s disease or Alzheimer’s disease. To propagate in disease, these misfolded protein aggregates must grow and divide to proliferate. Therefore, the intrinsic characteristics of their division, including the division rate and the pattern of division in terms of whether the fibrils are likely to break in the middle or at the edges, impact the disease aetiology. Here, we discovered mathematical formulae that can be used to directly extract the fibril division characteristics from recent experiments data obtained from time-dependent fibril length distribution measurements. We explain how these formulae can be used, and prove the robustness of the division rate formula where small errors in the measurement leads to small errors in the division rate. We also demonstrate that the mathematical formula is not robust enough to precisely decipher the pattern of division in the data, and suggest instead new future experimental design with short time measurements in experiments starting with fibril suspensions where all fibrils have similar size, which would be suitable to provide improved estimates.

Secondary Nucleation and the Conservation of Structural Characteristics of Amyloid Fibril Strains

Amyloid fibrils are ordered protein aggregates and a hallmark of many severe neurodegenerative diseases. Amyloid fibrils form through primary nucleation from monomeric protein, grow through monomer addition and proliferate through fragmentation or through the nucleation of new fibrils on the surface of existing fibrils (secondary nucleation). It is currently still unclear how amyloid fibrils initially form in the brain of affected individuals and how they are amplified. A given amyloid protein can sometimes form fibrils of different structure under different solution conditions in vitro, but often fibrils found in patients are highly homogeneous. These findings suggest that the processes that amplify amyloid fibrils in vivo can in some cases preserve the structural characteristics of the initial seed fibrils. It has been known for many years that fibril growth by monomer addition maintains the structure of the seed fibril, as the latter acts as a template that imposes its fold on the newly added monomer. However, for fibrils that are formed through secondary nucleation it was, until recently, not clear whether the structure of the seed fibril is preserved. Here we review the experimental evidence on this question that has emerged over the last years. The overall picture is that the fibril strain that forms through secondary nucleation is mostly defined by the solution conditions and intrinsic structural preferences, and not by the seed fibril strain.

Computational Model for Studying Breakage-Dependent Amyloid Growth

Amyloid fibrils are typically associated with neurodegenerative diseases. Recent studies have suggested that, similar to prions, many amyloid proteins are infectious in nature and may cause spreading and dissemination of diseases. Typical amyloid infection propagates by recruiting functional proteins into amyloidogenic form and multiplying by breaking the existing fibril. In this study, we model the kinetics of fibril growth through breakage and the subsequent elongation process, similar to the prion infection process. Using kinetic Monte Carlo simulations as well as mathematical counting methods, we show how the measurable quantities like the 50% aggregation time (T₅₀) and the maximum growth rate (V_max) scale with various parameters in the problem. This study has a direct application where it can be used to understand experiments that amplify the minute amount of amyloid seeds present in biological fluid for early detection of human disease. Using the knowledge from our simulations, we can predict the initial seed concentration, known as the filament kinetics.

The Division of Amyloid Fibrils: Systematic Comparison of Fibril Fragmentation Stability by Linking Theory with Experiments

The division of amyloid protein fibrils is required for the propagation of the amyloid state and is an important contributor to their stability, pathogenicity, and normal function. Here, we combine kinetic nanoscale imaging experiments with analysis of a mathematical model to resolve and compare the division stability of amyloid fibrils. Our theoretical results show that the division of any type of filament results in self-similar length distributions distinct to each fibril type and the conditions applied. By applying these theoretical results to profile the dynamical stability toward breakage for four different amyloid types, we reveal particular differences in the division properties of disease-related amyloid formed from α-synuclein when compared with non-disease associated model amyloid, the former showing lowered intrinsic stability toward breakage and increased likelihood of shedding smaller particles. Our results enable the comparison of protein filaments' intrinsic dynamic stabilities, which are key to unraveling their toxic and infectious potentials.

How and why to build a mathematical model: A case study using prion aggregation

Biological systems are inherently complex, and the increasing level of detail with which we are able to experimentally probe such systems continually reveals new complexity. Fortunately, mathematical models are uniquely positioned to provide a tool suitable for rigorous analysis, hypothesis generation, and connecting results from isolated in vitro experiments with results from in vivo and whole-organism studies. However, developing useful mathematical models is challenging because of the often different domains of knowledge required in both math and biology. In this work, we endeavor to provide a useful guide for researchers interested in incorporating mathematical modeling into their scientific process. We advocate for the use of conceptual diagrams as a starting place to anchor researchers from both domains. These diagrams are useful for simplifying the biological process in question and distinguishing the essential components. Not only do they serve as the basis for developing a variety of mathematical models, but they ensure that any mathematical formulation of the biological system is led primarily by scientific questions. We provide a specific example of this process from our own work in studying prion aggregation to show the power of mathematical models to synergistically interact with experiments and push forward biological understanding. Choosing the most suitable model also depends on many different factors, and we consider how to make these choices based on different scales of biological organization and available data. We close by discussing the many opportunities that abound for both experimentalists and modelers to take advantage of collaborative work in this field.

Polymer-Peptide Conjugates Convert Amyloid into Protein Nanobundles through Fragmentation and Lateral Association

The assembly of proteins into amyloid fibrils has become linked not only with the progression of myriad human diseases, but also important biological functions. Understanding and controlling the formation, structure, and stability of amyloid fibrils is therefore a major scientific goal. Here we utilize electron microscopy-based approaches combined with quantitative statistical analysis to show how recently developed kind of amyloid modulators-multivalent polymer-peptide conjugates (mPPCs)-can be applied to control the structure and stability of amyloid fibrils. In doing so, we demonstrate that mPPCs are able to convert 40-residue amyloid beta fibrils into ordered nanostructures through a combination of fragmentation and bundling. Fragmentation is shown to be consistent with a model where the rate constant of fibril breakage is independent of the fibril length, suggesting a local and specific interaction between fibrils and mPPCs. Subsequent bundling, which was previously not observed, leads to the formation of sheet-like nanostructures which are surprisingly much more uniform than the starting fibrils. These nanostructures have dimensions independent of the molecular weight of the mPPC and retain the molecular-level ordering of the starting amyloid fibrils. Collectively, we reveal quantitative and nanoscopic understanding of how mPPCs can be applied to control amyloid structure and stability, and demonstrate approaches to elucidate nanoscale amyloid phase behavior in the presence of functional macromolecules and other modulators.

The growth of amyloid fibrils: rates and mechanisms

Amyloid fibrils are β-sheet-rich linear protein polymers that can be formed by a large variety of different proteins. These assemblies have received much interest in recent decades, due to their role in a range of human disorders. However, amyloid fibrils are also found in a functional context, whereby their structural, mechanical and thermodynamic properties are exploited by biological systems. Amyloid fibrils form through a nucleated polymerisation mechanism with secondary processes acting in many cases to amplify the number of fibrils. The filamentous nature of amyloid fibrils implies that the fibril growth rate is, by several orders of magnitude, the fastest step of the overall aggregation reaction. This article focusses specifically on in vitro experimental studies of the process of amyloid fibril growth, or elongation, and summarises the state of knowledge of its kinetics and mechanisms. This work attempts to provide the most comprehensive summary, to date, of the available experimental data on amyloid fibril elongation rate constants and the temperature and concentration dependence of amyloid fibril elongation rates. These data are compared with those from other types of protein polymers. This comparison with data from other polymerising proteins is interesting and relevant because many of the basic ideas and concepts discussed here were first introduced for non-amyloid protein polymers, most notably by the Japanese school of Oosawa and co-workers for cytoskeletal filaments.

A first-passage approach to the thermal breakage of a discrete one-dimensional chain

Using the first passage method for a Markov process, we theoretically study the fragmentation rate of a discrete one-dimensional chain (Rouse model). The fragmentation occurs due to thermal fluctuations. Assuming equilibrium initial conditions, we obtain an expression for the fragmentation rate of the one-dimensional filament as a function of the number of monomers, the position of the breaking point along the filament, the ratio of the bond energy to the thermal energy, and the Rouse relaxation time. We also obtain the fragmentation rate for a fixed initial configuration of the chain by numerically solving a Volterra equation. Our results reduce to those of previous theoretical studies at the appropriate limits, and spell out the role of the relevant time scales. The prediction of our model for the fragmentation rate of insulin fibrils under optimal growth conditions for the solution appears to be consistent with experimental data from other studies.

The role of annealing and fragmentation in human tau aggregation dynamics

Alzheimer's disease pathogenesis is associated with the conversion of monomeric tau protein into filamentous aggregates. Because both toxicity and prion-like spread of pathogenic tau depend in part on aggregate size, the processes that underlie filament formation and size distribution are of special importance. Here, using a combination of biophysical and computational approaches, we investigated the fibrillation dynamics of the human tau isoform 2N4R. We found that tau filaments engage in a previously uncharacterized secondary process involving end-to-end annealing and that rationalization of empirical aggregation data composed of total protomer concentrations and fibril length distributions requires inclusion of this process along with filament fragmentation. We noted that annealing of 2N4R tau filaments is robust, with an intrinsic association rate constant of a magnitude similar to that mediating monomer addition and consistent with diffusion-mediated protein-protein interactions in the absence of long-range attractive forces. In contrast, secondary nucleation on the surface of tau filaments did not detectably contribute to tau aggregation dynamics. These results indicate that tau filament ends engage in a range of homotypic interactions involving monomers, oligomers, and filaments. They further indicate that, in the case of tau protein, fibril annealing and fragmentation along with primary nucleation and elongation are the major processes controlling filament size distribution.

Methods for Structural Analysis of Amyloid Fibrils in Misfolding Diseases

Many proteins and peptides are able to self-assemble in solution in vitro and in vivo to form amyloid-like fibrils. These fibrils share common structural characteristics. In order for a fibril to be characterized as amyloid, it is expected to fit certain criteria including the composition of cross-β. Here we describe how the formation of amyloid fibrils can be characterized in vitro using a variety of methods including circular dichroism and intrinsic tyrosine/tryptophan fluoresence to follow conformational changes; Thioflavin and/or ThS assembly to monitor nucleation and growth; transmission electron microscopy to visualize fibrillar morphology and X-ray fiber diffraction to examine cross-β structure.

On the Applicability of Force Fields To Study the Aggregation of Amyloidogenic Peptides Using Molecular Dynamics Simulations

Molecular dynamics simulations play an essential role in understanding biomolecular processes such as protein aggregation at temporal and spatial resolutions which are not attainable by experimental methods. For a correct modeling of protein aggregation, force fields must accurately represent molecular interactions. Here, we study the effect of five different force fields on the oligomer formation of Alzheimer's Aβ_16-22 peptide and two of its mutants: Aβ_16-22(F19V,F20V), which does not form fibrils, and Aβ_16-22(F19L) which forms fibrils faster than the wild type. We observe that while oligomer formation kinetics depends strongly on the force field, structural properties, such as the most relevant protein-protein contacts, are similar between them. The oligomer formation kinetics obtained with different force fields differ more from each other than the kinetics between aggregating and nonaggregating peptides simulated with a single force field. We discuss the difficulties in comparing atomistic simulations of amyloid oligomer formation with experimental observables.

The structure of a β2-microglobulin fibril suggests a molecular basis for its amyloid polymorphism

All amyloid fibrils contain a cross-β fold. How this structure differs in fibrils formed from proteins associated with different diseases remains unclear. Here, we combine cryo-EM and MAS-NMR to determine the structure of an amyloid fibril formed in vitro from β₂-microglobulin (β₂m), the culprit protein of dialysis-related amyloidosis. The fibril is composed of two identical protofilaments assembled from subunits that do not share β₂m's native tertiary fold, but are formed from similar β-strands. The fibrils share motifs with other amyloid fibrils, but also contain unique features including π-stacking interactions perpendicular to the fibril axis and an intramolecular disulfide that stabilises the subunit fold. We also describe a structural model for a second fibril morphology and show that it is built from the same subunit fold. The results provide insights into the mechanisms of fibril formation and the commonalities and differences within the amyloid fold in different protein sequences.

Measurement of Tau Filament Fragmentation Provides Insights into Prion-like Spreading

The ordered assembly of amyloidogenic proteins causes a wide spectrum of common neurodegenerative diseases, including Alzheimer's and Parkinson's diseases. These diseases share common features with prion diseases, in which misfolded proteins can self-replicate and transmit disease across different hosts. Deciphering the molecular mechanisms that underlie the amplification of aggregates is fundamental for understanding how pathological deposits can spread through the brain and drive disease. Here, we used single-molecule microscopy to study the assembly and replication of tau at the single aggregate level. We found that tau aggregates have an intrinsic ability to amplify by filament fragmentation, and determined the doubling times for this replication process by kinetic modeling. We then simulated the spreading time for aggregates through the brain and found this to be in good agreement with both the observed time frame for spreading of pathological tau deposits in Alzheimer's disease and in experimental models of tauopathies. With this work we begin to understand the physical parameters that govern the spreading rates of tau and other amyloids through the human brain.

A Free Energy Barrier Caused by the Refolding of an Oligomeric Intermediate Controls the Lag Time of Amyloid Formation by hIAPP

Transiently populated oligomers formed en route to amyloid fibrils may constitute the most toxic aggregates associated with many amyloid-associated diseases. Most nucleation theories used to describe amyloid aggregation predict low oligomer concentrations and do not take into account free energy costs that may be associated with structural rearrangements between the oligomer and fiber states. We have used isotope labeling and two-dimensional infrared spectroscopy to spectrally resolve an oligomeric intermediate during the aggregation of the human islet amyloid protein (hIAPP or amylin), the protein associated with type II diabetes. A structural rearrangement includes the F₂₃G₂₄A₂₅I₂₆L₂₇ region of hIAPP, which starts from a random coil structure, evolves into ordered β-sheet oligomers containing at least 5 strands, and then partially disorders in the fibril structure. The supercritical concentration is measured to be between 150 and 250 μM, which is the thermodynamic parameter that sets the free energy of the oligomers. A 3-state kinetic model fits the experimental data, but only if it includes a concentration independent free energy barrier >3 kcal/mol that represents the free energy cost of refolding the oligomeric intermediate into the structure of the amyloid fibril; i.e., "oligomer activation" is required. The barrier creates a transition state in the free energy landscape that slows fibril formation and creates a stable population of oligomers during the lag phase, even at concentrations below the supercritical concentration. Largely missing in current kinetic models is a link between structure and kinetics. Our experiments and modeling provide evidence that protein structural rearrangements during aggregation impact the populations and kinetics of toxic oligomeric species.

The physical dimensions of amyloid aggregates control their infective potential as prion particles

Transmissible amyloid particles called prions are associated with infectious prion diseases in mammals and inherited phenotypes in yeast. All amyloid aggregates can give rise to potentially infectious seeds that accelerate their growth. Why some amyloid seeds are highly infectious prion particles while others are less infectious or even inert, is currently not understood. To address this question, we analyzed the suprastructure and dimensions of synthetic amyloid fibrils assembled from the yeast (Saccharomyces cerevisiae) prion protein Sup35NM. We then quantified the ability of these particles to induce the [PSI⁺] prion phenotype in cells. Our results show a striking relationship between the length distribution of the amyloid fibrils and their ability to induce the heritable [PSI⁺] prion phenotype. Using a simple particle size threshold model to describe transfection activity, we explain how dimensions of amyloid fibrils are able to modulate their infectious potential as prions.

Self-assembling peptide and protein amyloids: from structure to tailored function in nanotechnology

Self-assembled peptide and protein amyloid nanostructures have traditionally been considered only as pathological aggregates implicated in human neurodegenerative diseases. In more recent times, these nanostructures have found interesting applications as advanced materials in biomedicine, tissue engineering, renewable energy, environmental science, nanotechnology and material science, to name only a few fields. In all these applications, the final function depends on: (i) the specific mechanisms of protein aggregation, (ii) the hierarchical structure of the protein and peptide amyloids from the atomistic to mesoscopic length scales and (iii) the physical properties of the amyloids in the context of their surrounding environment (biological or artificial). In this review, we will discuss recent progress made in the field of functional and artificial amyloids and highlight connections between protein/peptide folding, unfolding and aggregation mechanisms, with the resulting amyloid structure and functionality. We also highlight current advances in the design and synthesis of amyloid-based biological and functional materials and identify new potential fields in which amyloid-based structures promise new breakthroughs.

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.

The involvement of dityrosine crosslinking in α-synuclein assembly and deposition in Lewy Bodies in Parkinson's disease

Parkinson’s disease (PD) is characterized by intracellular, insoluble Lewy bodies composed of highly stable α-synuclein (α-syn) amyloid fibrils. α-synuclein is an intrinsically disordered protein that has the capacity to assemble to form β-sheet rich fibrils. Oxidiative stress and metal rich environments have been implicated in triggering assembly. Here, we have explored the composition of Lewy bodies in post-mortem tissue using electron microscopy and immunogold labeling and revealed dityrosine crosslinks in Lewy bodies in brain tissue from PD patients. In vitro, we show that dityrosine cross-links in α-syn are formed by covalent ortho-ortho coupling of two tyrosine residues under conditions of oxidative stress by fluorescence and confirmed using mass-spectrometry. A covalently cross-linked dimer isolated by SDS-PAGE and mass analysis showed that dityrosine dimer was formed via the coupling of Y39-Y39 to give a homo dimer peptide that may play a key role in formation of oligomeric and seeds for fibril formation. Atomic force microscopy analysis reveals that the covalent dityrosine contributes to the stabilization of α-syn assemblies. Thus, the presence of oxidative stress induced dityrosine could play an important role in assembly and toxicity of α-syn in PD.

Estimation from moments measurements for amyloid depolymerisation

Estimating reaction rates and size distributions of protein polymers is an important step for understanding the mechanisms of protein misfolding and aggregation, a key feature for amyloid diseases. This study aims at setting this framework problem when the experimental measurements consist in the time-dynamics of a moment of the population (i.e. for instance the total polymerised mass, as in Thioflavin T measurements, or the second moment measured by Static Light Scattering). We propose a general methodology, and we solve the problem theoretically and numerically in the case of a depolymerising system. We then apply our method to experimental data of depolymerising oligomers, and conclude that smaller aggregates of ovPrP protein should be more stable than larger ones. This has an important biological implication, since it is commonly admitted that small oligomers constitute the most cytotoxic species during prion misfolding process.

Analysis of the length distribution of amyloid fibrils by centrifugal sedimentation

The aggregation of normally soluble peptides and proteins into amyloid fibrils is a process associated with a wide range of pathological conditions, including Alzheimer's and Parkinson's diseases. It has become apparent that aggregates of different sizes possess markedly different biological effects, with aggregates of lower relative molecular weight being associated with stronger neurotoxicity. Yet, although many approaches exist to measure the total mass concentration of aggregates, the ability to probe the length distribution of growing aggregates in solution has remained more elusive. In this work, we applied a differential centrifugation technique to measure the sedimentation coefficients of amyloid fibrils produced during the aggregation process of the amyloid β (M1-42) peptide (Aβ42). The centrifugal method has the advantage of providing structural information on the fibril distribution directly in solution and affording a short analysis time with respect to alternative imaging and analytical centrifugation approaches. We show that under quiescent conditions interactions between Aβ42 fibrils lead to lateral association and to the formation of entangled clusters. By contrast, aggregation under shaking generates a population of filaments characterized by shorter lengths. The results, which have been validated by cryogenic transmission electron microscopy (cryo-TEM) analysis, highlight the important role that fibril-fibril assembly can play in the deposition of aggregation-prone peptides.

α-Synuclein and huntingtin exon 1 amyloid fibrils bind laterally to the cellular membrane

Fibrillar aggregates involved in neurodegenerative diseases have the ability to spread from one cell to another in a prion-like manner. The underlying molecular mechanisms, in particular the binding mode of the fibrils to cell membranes, are poorly understood. In this work we decipher the modality by which aggregates bind to the cellular membrane, one of the obligatory steps of the propagation cycle. By characterizing the binding properties of aggregates made of α-synuclein or huntingtin exon 1 protein displaying similar composition and structure but different lengths to mammalian cells we demonstrate that in both cases aggregates bind laterally to the cellular membrane, with aggregates extremities displaying little or no role in membrane binding. Lateral binding to artificial liposomes was also observed by transmission electron microscopy. In addition we show that although α-synuclein and huntingtin exon 1 fibrils bind both laterally to the cellular membrane, their mechanisms of interaction differ. Our findings have important implications for the development of future therapeutic tools that aim to block protein aggregates propagation in the brain.

Thermal breakage of a semiflexible polymer: breakage profile and rate

Understanding fluctuation-induced breakages in polymers has important implications for basic and applied sciences. Here I present for the first time an analytical treatment of the thermal breakage problem of a semi-flexible polymer model that is asymptotically exact in the low temperature and high friction limits. Specifically, I provide analytical expressions for the breakage propensity and rate, and discuss the generalities of the results and their relevance to biopolymers. This work is fundamental to our understanding of the kinetics of living polymerisation.

Analysis of Toxic Amyloid Fibril Interactions at Natively Derived Membranes by Ellipsometry

There is an ongoing debate regarding the culprits of cytotoxicity associated with amyloid disorders. Although small pre-fibrillar amyloid oligomers have been implicated as the primary toxic species, the fibrillar amyloid material itself can also induce cytotoxicity. To investigate membrane disruption and cytotoxic effects associated with intact and fragmented fibrils, the novel in situ spectroscopic technique of Total Internal Reflection Ellipsometry (TIRE) was used. Fibril lipid interactions were monitored using natively derived whole cell membranes as a model of the in vivo environment. We show that fragmented fibrils have an increased ability to disrupt these natively derived membranes by causing a loss of material from the deposited surface when compared with unfragmented fibrils. This effect was corroborated by observations of membrane disruption in live cells, and by dye release assay using synthetic liposomes. Through these studies we demonstrate the use of TIRE for the analysis of protein-lipid interactions on natively derived lipid surfaces, and provide an explanation on how amyloid fibrils can cause a toxic gain of function, while entangled amyloid plaques exert minimal biological activity.

Information content in data sets for a nucleated-polymerization model

We illustrate the use of statistical tools (asymptotic theories of standard error quantification using appropriate statistical models, bootstrapping, and model comparison techniques) in addition to sensitivity analysis that may be employed to determine the information content in data sets. We do this in the context of recent models [S. Prigent, A. Ballesta, F. Charles, N. Lenuzza, P. Gabriel, L.M. Tine, H. Rezaei, and M. Doumic, An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation, PLoS ONE 7 (2012), e43273. doi:10.1371/journal.pone.0043273.] for nucleated polymerization in proteins, about which very little is known regarding the underlying mechanisms; thus, the methodology we develop here may be of great help to experimentalists. We conclude that the investigated data sets will support with reasonable levels of uncertainty only the estimation of the parameters related to the early steps of the aggregation process.

Fragmentation of amyloid fibrils occurs in preferential positions depending on the environmental conditions

Understanding the mechanism of amyloid fibril breakage is of fundamental importance in various research fields including biomedicine and bionanotechnology. The aim of this work is to clarify the impact of temperature and agitation speed on the fibril breakage rate constant, which depends both on the fibril length as well as on the position of fragmentation along the fibril longitudinal axis. In particular, we intend to discriminate between three fibril fragmentation mechanisms: erosion (i.e., breakage occurs preferentially at the ends of the fibril), random (i.e., breakage occurs with the same likelihood at any position), or central (i.e., breakage occurs preferentially at the center of the fibril). To do so, we compare the time evolution of the fibril length distribution followed with atomic force microscopy with simulations from a kinetic model based on population balance equations (PBE). In this frame, we investigate the breakage mechanism of insulin fibrils, which turns out to be affected by the operative conditions employed. Moreover, we compare our findings with literature data obtained with β-lactoglobulin and β2-microglobulin. It is observed that high temperature drives the breakage toward an erosion mechanism, while a high agitation rate rather induces a central breakage.

Nanomechanics and intermolecular forces of amyloid revealed by four-dimensional electron microscopy

The amyloid state of polypeptides is a stable, highly organized structural form consisting of laterally associated β-sheet protofilaments that may be adopted as an alternative to the functional, native state. Identifying the balance of forces stabilizing amyloid is fundamental to understanding the wide accessibility of this state to peptides and proteins with unrelated primary sequences, various chain lengths, and widely differing native structures. Here, we use four-dimensional electron microscopy to demonstrate that the forces acting to stabilize amyloid at the atomic level are highly anisotropic, that an optimized interbackbone hydrogen-bonding network within β-sheets confers 20 times more rigidity on the structure than sequence-specific sidechain interactions between sheets, and that electrostatic attraction of protofilaments is only slightly stronger than these weak amphiphilic interactions. The potential biological relevance of the deposition of such a highly anisotropic biomaterial in vivo is discussed.

Single fibril growth kinetics of α-synuclein

Neurodegenerative disorders associated with protein misfolding are fatal diseases that are caused by fibrillation of endogenous proteins such as α-synuclein (α-syn) in Parkinson's disease (PD) or amyloid-β in Alzheimer's disease. Fibrils of α-syn are a major pathological hallmark of PD and certain aggregation intermediates are postulated to cause synaptic failure and cell death of dopaminergic neurons in the substantia nigra. For the development of therapeutic approaches, the mechanistic understanding of the fibrillation process is essential. Here we report real-time observation of α-syn fibril elongation on a glass surface, imaged by total internal reflection fluorescence microscopy using thioflavin T fluorescence. Fibrillation on the glass surface occurred in the same time frame and yielded fibrils of similar length as fibrillation in solution. Time-resolved imaging of fibrillation on a single fibril level indicated that α-syn fibril elongation follows a stop-and-go mechanism; that is, fibrils either extend at a homogenous growth rate or stop to grow for variable time intervals. The fibril growth kinetics were compatible with a model featuring two states, a growth state and a stop state, which were approximately isoenergetic and interconverted with rate constants of ~1.5×10(-4) s(-1). In the growth state, α-syn monomers were incorporated into the fibril with a rate constant of 8.6×10(3) M(-1) s(-1). Fibril elongation of α-syn is slow compared to other amyloidogenic proteins.

The binding of apolipoprotein E to oligomers and fibrils of amyloid-β alters the kinetics of amyloid aggregation

Deposition of amyloid-β (Aβ) in Alzheimer’s disease (AD) is strongly correlated with the APOE genotype. However, the role of apolipoprotein E (apoE) in Aβ aggregation has remained unclear. Here we have used different apoE preparations, such as recombinant protein or protein isolated from cultured astrocytes, to examine the effect of apoE on the aggregation of both Aβ_1–40 and Aβ_1–42. The kinetics of aggregation, measured by the loss of fluorescence of tetramethylrhodamine-labeled Aβ, is shown to be dramatically slowed by the presence of substoichiometric concentrations of apoE. Using these concentrations, we conclude that apoE binds primarily to and affects the growth of oligomers that lead to the nuclei required for fibril growth. At higher apoE concentrations, the protein also binds to Aβ fibrils, resulting in fibril stabilization and a slower rate of fibril growth. The aggregation of Aβ_1–40 is dependent on the apoE isoform, being the most dramatic for apoE4 and less so for apoE3 and apoE2. Our results indicate that the detrimental role of apoE4 in AD could be related to apoE-induced stabilization of the soluble but cytotoxic oligomeric forms and intermediates of Aβ, as well as fibril stabilization.

The physical chemistry of the amyloid phenomenon: thermodynamics and kinetics of filamentous protein aggregation

In this chapter, we present an overview of the kinetics and thermodynamics of protein aggregation into amyloid fibrils. The perspective we adopt is largely experimental, but we also discuss recent developments in data analysis and we show that only a combination of well-designed experiments with appropriate theoretical modelling is able to provide detailed mechanistic insight into the complex pathways of amyloid formation. In the first part of the chapter, we describe measurements of the thermodynamic stability of the amyloid state with respect to the soluble state of proteins, as well as the magnitude and origin of this stability. In the second part, we discuss in detail the kinetics of the individual molecular steps in the overall mechanism of the conversion of soluble protein into amyloid fibrils. Finally, we highlight the effects of external factors, such as salt type and concentration, chemical denaturants and molecular chaperones on the kinetics of aggregation.

β2-Microglobulin amyloid fibril-induced membrane disruption is enhanced by endosomal lipids and acidic pH

Although the molecular mechanisms underlying the pathology of amyloidoses are not well understood, the interaction between amyloid proteins and cell membranes is thought to play a role in several amyloid diseases. Amyloid fibrils of β2-microglobulin (β2m), associated with dialysis-related amyloidosis (DRA), have been shown to cause disruption of anionic lipid bilayers in vitro. However, the effect of lipid composition and the chemical environment in which β2m-lipid interactions occur have not been investigated previously. Here we examine membrane damage resulting from the interaction of β2m monomers and fibrils with lipid bilayers. Using dye release, tryptophan fluorescence quenching and fluorescence confocal microscopy assays we investigate the effect of anionic lipid composition and pH on the susceptibility of liposomes to fibril-induced membrane damage. We show that β2m fibril-induced membrane disruption is modulated by anionic lipid composition and is enhanced by acidic pH. Most strikingly, the greatest degree of membrane disruption is observed for liposomes containing bis(monoacylglycero)phosphate (BMP) at acidic pH, conditions likely to reflect those encountered in the endocytic pathway. The results suggest that the interaction between β2m fibrils and membranes of endosomal origin may play a role in the molecular mechanism of β2m amyloid-associated osteoarticular tissue destruction in DRA.

The relationship between amyloid structure and cytotoxicity

Self-assembly of proteins and peptides into amyloid structures has been the subject of intense and focused research due to their association with neurodegenerative, age-related human diseases and transmissible prion diseases in humans and mammals. Of the disease associated amyloid assemblies, a diverse array of species, ranging from small oligomeric assembly intermediates to fibrillar structures, have been shown to have toxic potential. Equally, a range of species formed by the same disease associated amyloid sequences have been found to be relatively benign under comparable monomer equivalent concentrations and conditions. In recent years, an increasing number of functional amyloid systems have also been found. These developments show that not all amyloid structures are generically toxic to cells. Given these observations, it is important to understand why amyloid structures may encode such varied toxic potential despite sharing a common core molecular architecture. Here, we discuss possible links between different aspects of amyloidogenic structures and assembly mechanisms with their varied functional effects. We propose testable hypotheses for the relationship between amyloid structure and its toxic potential in the context of recent reports on amyloid sequence, structure, and toxicity relationships.

Solution conditions determine the relative importance of nucleation and growth processes in α-synuclein aggregation

The formation of amyloid fibrils by the intrinsically disordered protein α-synuclein is a hallmark of Parkinson disease. To characterize the microscopic steps in the mechanism of aggregation of this protein we have used in vitro aggregation assays in the presence of preformed seed fibrils to determine the molecular rate constant of fibril elongation under a range of different conditions. We show that α-synuclein amyloid fibrils grow by monomer and not oligomer addition and are subject to higher-order assembly processes that decrease their capacity to grow. We also find that at neutral pH under quiescent conditions homogeneous primary nucleation and secondary processes, such as fragmentation and surface-assisted nucleation, which can lead to proliferation of the total number of aggregates, are undetectable. At pH values below 6, however, the rate of secondary nucleation increases dramatically, leading to a completely different balance between the nucleation and growth of aggregates. Thus, at mildly acidic pH values, such as those, for example, that are present in some intracellular locations, including endosomes and lysosomes, multiplication of aggregates is much faster than at normal physiological pH values, largely as a consequence of much more rapid secondary nucleation. These findings provide new insights into possible mechanisms of α-synuclein aggregation and aggregate spreading in the context of Parkinson disease.

Kinetics of protein fibrillation controlled by fibril elongation

Numerous proteins have the ability to assemble into fibrillar aggregates which are of great interest, because they feature in scores of human diseases and many technological products. In the present work, we analyze the kinetics of protein fibrillation when the process is governed solely by elongation of initially appeared fibrils in the protein solution. We derive exact expressions for the time dependences of the fibrillation degree, the concentration of monomeric protein in the solution, and the average fibril size. Furthermore, we present formulas for the initial fibrillation rate and the half-fibrillation time in terms of experimentally controllable quantities. The results obtained provide a mechanistic insight into the kinetics of protein fibrillation mediated by fibril elongation. We confront theory with experiment and find that it allows a good description of available experimental data for fibrillation of the Alzheimer's disease-associated protein Aβ(1-40) and the yeast prion protein Sup35.