Atomistic theory of amyloid fibril nucleation

Protein Corona Formation and Aggregation of Amyloid β 1-40-Coated Gold Nanocolloids

Amyloid fibrillogenesis is a pathogenic protein aggregation process that occurs through a highly ordered process of protein-protein interactions. To better understand the protein-protein interactions involved in amyloid fibril formation, we formed nanogold colloid aggregates by stepwise additions of ∼2 nmol of amyloid β 1-40 peptide (Aβ1-40) at pH ∼3.7 and ∼25 °C. The processes of protein corona formation and building of gold colloid [diameters (d) of 20 and 80 nm] aggregates were confirmed by a red-shift of the surface plasmon resonance (SPR) band, λpeak, as the number of Aβ1-40 peptides [N(Aβ1-40)] increased. The normalized red-shift of λpeak, Δλ, was correlated with the degree of protein aggregation, and this process was approximated as the adsorption isotherm explained by the Langmuir-Freundlich model. As the coverage fraction (θ) was analyzed as a function of ϕ, which is the N(Aβ1-40) per total surface area of nanogold colloids available for adsorption, the parameters for explaining the Langmuir-Freundlich model were in good agreement for both 20 and 80 nm gold, indicating that ϕ could define the stage of the aggregation process. Surface-enhanced Raman scattering (SERS) imaging was conducted at designated values of ϕ and suggested that a protein-gold surface interaction during the initial adsorption stage may be dependent on the nanosize. The 20 nm gold case seems to prefer a relatively smaller contacting section, such as a -C-N or C═C bond, but a plane of the benzene ring may play a significant role for 80 nm gold. Regardless of the size of the particles, the β-sheet and random coil conformations were considered to be used to form gold colloid aggregates. The methodology developed in this study allows for new insights into protein-protein interactions at distinct stages of aggregation.

Quantification of Surface Tension Effects and Nucleation-and-Growth Rates during Self-Assembly of Biological Condensates

Liquid-solid and liquid-liquid phase separation (PS) drives the formation of functional and disease-associated biological assemblies. Principles of phase equilibrium are here employed to derive a general kinetic solution that predicts the evolution of the mass and size of biological assemblies. Thermodynamically, protein PS is determined by two measurable concentration limits: the saturation concentration and the critical solubility. Due to surface tension effects, the critical solubility can be higher than the saturation concentration for small, curved nuclei. Kinetically, PS is characterized by the primary nucleation rate constant and a combined rate constant accounting for growth and secondary nucleation. It is demonstrated that the formation of a limited number of large condensates is possible without active mechanisms of size control and in the absence of coalescence phenomena. The exact analytical solution can be used to interrogate how the elementary steps of PS are affected by candidate drugs.

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.

Dissection of the key steps of amyloid-β peptide 1-40 fibrillogenesis

The aggregation kinetics of Aβ1-40 peptide was characterized using a synergistic approach by a combination of nuclear magnetic resonance, thioflavin-T fluorescence, transmission electron microscopy and dynamic light scattering. A major finding is the experimental detection of high molecular weight oligomers (HMWO) that converts into fibrils nuclei. Our observations are consistent with a mechanism of Aβ1-40 fibrillogenesis that includes the following key steps: i) slow formation of HMWO (Rh ~ 20 nm); ii) conversion of the HMWO into more compact Rh ~ 10 nm fibrils nuclei; iii) fast formation of additional fibrils nuclei through fibril surface catalysed processes; and iv) growth of fibrils by addition of soluble Aβ species. Moreover, NMR diffusion experiments show that at 37 °C soluble Aβ1-40 remains intrinsically disordered and mostly in monomeric form despite evidences of the presence of dimers and/or other small oligomers. A mathematical model is proposed to simulate the aggregation kinetics of Aβ1-40.

The Kinetics, Thermodynamics and Mechanisms of Short Aromatic Peptide Self-Assembly

The self-assembly of short aromatic peptides and peptide derivatives into a variety of different nano- and microstructures (fibrillar gels, crystals, spheres, plates) is a promising route toward the creation of bio-compatible materials with often unexpected and useful properties. Furthermore, such simple self-assembling systems have been proposed as model systems for the self-assembly of longer peptides, a process that can be linked to biological function and malfunction. Much effort has been made in the last 15 years to explore the space of peptide sequences, chemical modifications and solvent conditions in order to maximise the diversity of assembly morphologies and properties. However, quantitative studies of the corresponding mechanisms of, and driving forces for, peptide self-assembly have remained relatively scarce until recently. In this chapter we review the current state of understanding of the thermodynamic driving forces and self-assembly mechanisms of short aromatic peptides into supramolecular structures. We will focus on experimental studies of the assembly process and our perspective will be centered around diphenylalanine (FF), a key motif of the amyloid β sequence and a paradigmatic self-assembly building block. Our main focus is the basic physical chemistry and key structural aspects of such systems, and we will also compare the mechanism of dipeptide aggregation with that of longer peptide sequences into amyloid fibrils, with discussion on how these mechanisms may be revealed through detailed analysis of growth kinetics, thermodynamics and other fundamental properties of the aggregation process.

Pre-aggregation kinetics and intermediates of α-synuclein monitored by the ESIPT probe 7MFE

The defining feature of the extensive family of amyloid diseases is the formation of networks of entangled elongated protein fibrils and amorphous aggregates exhibiting crossed β-sheet secondary structure. The time course of amyloid conversion has been studied extensively in vitro with the proteins involved in the neurodegenerative pathology of Parkinson's disease (α-synuclein), Alzheimer's disease (Tau) and Huntington's disease (Huntingtin). Although much is known about the thermodynamics and kinetics of the transition from a soluble, intrinsically disordered monomer to the fibrillar end state, the putative oligomeric intermediates, currently considered to be the major initiators of cellular toxicity, are as yet poorly defined. We have detected and characterized amyloid precursors by monitoring AS aggregation with ESIPT (excited state intramolecular protein transfer) probes, one of which, 7MFE [7-(3-maleimido-N-propanamide)-2-(4-diethyaminophenyl)-3-hydroxychromone], is introduced here and compared with a related compound, 6MFC, used previously. A series of 140 spectra for sparsely labeled AS was acquired during the course of aggregation, and resolved into the relative contributions (spectra, intensities) of discrete molecular species including the monomeric, fibrillar, and ensemble of intermediate forms. Based on these findings, a kinetic scheme was devised to simulate progress curves as a function of key parameters. An essential feature of the model, one not previously invoked in schemes of amyloid aggregation, is the catalysis of molecular fuzziness by discrete colloidal nanoparticles arising spontaneously via monomer condensation upon exposure of AS to ≥ 37 °C.

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.

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.

Protein Polymerization into Fibrils from the Viewpoint of Nucleation Theory

The assembly of various proteins into fibrillar aggregates is an important phenomenon with wide implications ranging from human disease to nanoscience. Using general kinetic results of nucleation theory, we analyze the polymerization of protein into linear or helical fibrils in the framework of the Oosawa-Kasai (OK) model. We show that while within the original OK model of linear polymerization the process does not involve nucleation, within a modified OK model it is nucleation-mediated. Expressions are derived for the size of the fibril nucleus, the work for fibril formation, the nucleation barrier, the equilibrium and stationary fibril size distributions, and the stationary fibril nucleation rate. Under otherwise equal conditions, this rate decreases considerably when the short (subnucleus) fibrils lose monomers much more frequently than the long (supernucleus) fibrils, a feature that should be born in mind when designing a strategy for stymying or stimulating fibril nucleation. The obtained dependence of the nucleation rate on the concentration of monomeric protein is convenient for experimental verification and for use in rate equations accounting for nucleation-mediated fibril formation. The analysis and the results obtained for linear fibrils are fully applicable to helical fibrils whose formation is describable by a simplified OK model.

Pseudo-one-dimensional nucleation in dilute polymer solutions

Pathogenic protein fibrils have been shown in vitro to have nucleation-dependent kinetics despite the fact that one-dimensional structures do not have the size-dependent surface energy responsible for the lag time in classical theory. We present a theory showing that the conformational entropy of the peptide chains creates a free-energy barrier that is analogous to the translational entropy barrier in higher dimensions. We find that the dynamics of polymer rearrangement make it very unlikely for nucleation to succeed along the lowest free-energy trajectory, meaning that most of the nucleation flux avoids the free-energy saddle point. We use these results to construct a three-dimensional model for amyloid nucleation that accounts for conformational entropy, backbone H bonds, and side-chain interactions to compute nucleation rates as a function of concentration.

Prediction of a stable associated liquid of short amyloidogenic peptides

Amyloid fibril formation is believed to be a nucleation-controlled process. Depending on the nature of peptide sequence, fibril nucleation can occur in one step, straight from a dilute solution, or in multiple steps via oligomers or disordered aggregates. What determines this process is poorly understood. Since the fibril formation kinetics is driven by thermodynamic forces, knowledge of the phase behavior is crucial. Here, we investigated the phase behavior of three short peptide sequences of varying side-chain hydrophobicity. Replica exchange molecular dynamics simulations of a mid-resolution model indicate that the weakly hydrophobic peptide forms fibrils directly from solution, whereas the most hydrophobic peptide forms a dense liquid phase before crystallizing into ordered fibrils at low temperatures. For the medium hydrophobic peptide we found evidence of a novel additional transition to a liquid phase consisting of clusters of aligned peptides, implying a three-step nucleation process. We tested the robustness of this prediction by applying Wertheim's theory and statistical associating fluid theory to a hard-sphere model dressed with isotropic and anisotropic attractions. We found that the ratio of interaction strengths strongly affects the phase behavior, and under certain conditions indeed gives rise to a stable polymerized liquid phase. The peptide clusters in the associated liquid tend to be slow and long-lived, which may give the oligomer droplet more time to act as a toxic oligomer, before turning into a fibril.

Nucleation of polymorphic amyloid fibrils

One and the same protein can self-assemble into amyloid fibrils with different morphologies. The phenomenon of fibril polymorphism is relevant biologically because different fibril polymorphs can have different toxicity, but there is no tool for predicting which polymorph forms and under what conditions. Here, we consider the nucleation of polymorphic amyloid fibrils occurring by direct polymerization of monomeric proteins into fibrils. We treat this process within the framework of our newly developed nonstandard nucleation theory, which allows prediction of the concentration dependence of the nucleation rate for different fibril polymorphs. The results highlight that the concentration dependence of the nucleation rate is closely linked with the protein solubility and a threshold monomer concentration below which fibril formation becomes biologically irrelevant. The relation between the nucleation rate, the fibril solubility, the threshold concentration, and the binding energies of the fibril building blocks within fibrils might prove a valuable tool for designing new experiments to control the formation of particular fibril polymorphs.

Heat of supersaturation-limited amyloid burst directly monitored by isothermal titration calorimetry

Amyloid fibrils form in supersaturated solutions via a nucleation and growth mechanism. Although the structural features of amyloid fibrils have become increasingly clearer, knowledge on the thermodynamics of fibrillation is limited. Furthermore, protein aggregation is not a target of calorimetry, one of the most powerful approaches used to study proteins. Here, with β2-microglobulin, a protein responsible for dialysis-related amyloidosis, we show direct heat measurements of the formation of amyloid fibrils using isothermal titration calorimetry (ITC). The spontaneous fibrillation after a lag phase was accompanied by exothermic heat. The thermodynamic parameters of fibrillation obtained under various protein concentrations and temperatures were consistent with the main-chain dominated structural model of fibrils, in which overall packing was less than that of the native structures. We also characterized the thermodynamics of amorphous aggregation, enabling the comparison of protein folding, amyloid fibrillation, and amorphous aggregation. These results indicate that ITC will become a promising approach for clarifying comprehensively the thermodynamics of protein folding and misfolding.

Confounding the paradigm: peculiarities of amyloid fibril nucleation

Fibrils of amyloid proteins are currently of great interest because of their involvement in various amyloid-related diseases and nanotechnological products. In a recent kinetic Monte Carlo simulation study (Cabriolu, R.; Kashchiev, D.; Auer, S. J. Chem. Phys.2012, 137, 204903), we found that our simulation data for the rate of amyloid fibril nucleation occurring by direct polymerization of monomeric protein could not be described adequately by nucleation theory. It turned out that the process occurred in a peculiar way, thus confounding the nucleation paradigm and demanding a new theoretical treatment. In the present study, we reconsider the theoretical approach to nucleation of amyloid fibrils and derive new expressions for the stationary rate of the process. As these expressions provide a remarkably good description of the simulation data, by using them we propose a theoretical dependence of the amyloid-β(40) fibril nucleation rate on the concentration of monomeric protein in the solution. This dependence reveals the existence of a threshold concentration below which the fibril nucleation in small enough solution volumes is practically arrested, and above which the process occurs vigorously, because then each monomeric protein in the solution acts as fibril nucleus. The presented expressions for the threshold concentration and for the dependence of the fibril nucleation rate on the concentration of monomeric protein can be a valuable guide in designing new therapeutic and/or technological strategies for prevention or stimulation of amyloid fibril formation.

Length distribution of stiff, self-assembled polymers at thermal equilibrium

We investigate the length distribution of self-assembled, long and stiff polymers at thermal equilibrium. Our analysis is based on calculating the partition functions of stiff polymers of variable lengths in the elastic regime. Our conclusion is that the length distribution of this self-assembled system follows closely the exponential distribution, except at the short length limit. We then discuss the implications of our results on the experimentally observed length distributions in amyloid fibrils.

Distinguishing crystal-like amyloid fibrils and glass-like amorphous aggregates from their kinetics of formation

Amyloid fibrils and amorphous aggregates are two types of aberrant aggregates associated with protein misfolding diseases. Although they differ in morphology, the two forms are often treated indiscriminately. β(2)-microglobulin (β2m), a protein responsible for dialysis-related amyloidosis, forms amyloid fibrils or amorphous aggregates depending on the NaCl concentration at pH 2.5. We compared the kinetics of their formation, which was monitored by measuring thioflavin T fluorescence, light scattering, and 8-anilino-1-naphthalenesulfonate fluorescence. Thioflavin T fluorescence specifically monitors amyloid fibrillation, whereas light scattering and 8-anilino-1-naphthalenesulfonate fluorescence monitor both amyloid fibrillation and amorphous aggregation. The amyloid fibrils formed via a nucleation-dependent mechanism in a supersaturated solution, analogous to crystallization. The lag phase of fibrillation was reduced upon agitation with stirring or ultrasonic irradiation, and disappeared by seeding with preformed fibrils. In contrast, the glass-like amorphous aggregates formed rapidly without a lag phase. Neither agitation nor seeding accelerated the amorphous aggregation. Thus, by monitoring the kinetics, we can distinguish between crystal-like amyloid fibrils and glass-like amorphous aggregates. Solubility and supersaturation will be key factors for further understanding the aberrant aggregation of proteins.

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

Amyloid protein fibrils feature in various diseases and nanotechnological products. Currently, it is debated whether they nucleate in one step (i.e., directly from the protein solution) or in two steps (step one being the appearance of nonfibrillar oligomers in the solution and step two being the oligomer conversion into fibrils). We employ nucleation theory to gain insight into the idiosyncrasy of two-step fibril nucleation and to determine the conditions under which this process can take place. Presenting an expression for the rate of two-step fibril nucleation, we use it to qualitatively describe experimental data for two-step nucleated amyloid-β fibrils. Our analysis helps in understanding why, in some experiments, oligomers rather than fibrils form and remain structurally unchanged and why, in others, the oligomers convert into fibrils.

Size distribution of amyloid nanofibrils

We consider the size distribution of amyloid nanofibrils (protofilaments) in nucleating protein solutions when the nucleation process occurs by the mechanism of direct polymerization of β-strands (extended peptides or protein segments) into β-sheets. Employing the atomistic nucleation theory, we derive a general expression for the stationary size distribution of amyloid nanofibrils constituted of successively layered β-sheets. The application of this expression to amyloid β(1-40) (Aβ(40)) fibrils allows us to determine the nanofibril size distribution as a function of the protein concentration and temperature. The distribution is most remarkable with its exhibiting a series of peaks positioned at "magic" nanofibril sizes (or lengths), which are due to deep local minima in the work for fibril formation. This finding of magic sizes or lengths is consistent with experimental results for the size distribution of aggregates in solutions of Aβ(40) proteins. Also, our approach makes it possible to gain insight into the effect of point mutations on the nanofibril size distribution, an effect that may play a role in experimentally observed substantial differences in the fibrillation lag-time of wild-type and point-mutated amyloid-β proteins.