Amyloid Fibrillation Kinetics: Insight from Atomistic Nucleation Theory

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.

Assembly Mechanism for Aggregation of Amyloid Fibrils

The assembly mechanism for aggregation of amyloid fibril is important and fundamental for any quantitative and physical descriptions because it needs to have a deep understanding of both molecular and statistical physics. A theoretical model with three states including coil, helix and sheet is presented to describe the amyloid formation. The corresponding general mathematical expression of N molecule systems are derived, including the partition function and thermodynamic quantities. We study the equilibrium properties of the system in the solution and find that three molecules have the extreme value of free energy. The denaturant effect on molecular assemble is also discussed. Furthermore, we apply the kinetic theories to take account of the nucleation and growth of the amyloid in the solution. It has been shown that our theoretical results can be compared with experimental results.

Common molecular pathogenesis of disease-related intrinsically disordered proteins revealed by NMR analysis

Intrinsically disordered proteins (IDPs) are either completely unstructured or contain large disordered regions in their native state; they have drawn much attention in the field of molecular pathology. Some of them substantially tend to form protein self-assemblies, such as toxic or non-toxic aggregates and fibrils, and have been postulated to relate to diseases. These disease-related IDPs include Aβ(1-42) [Alzheimer's disease (AD)], Tau (AD and tauopathy), α-synuclein (Parkinson's disease) and p53 (cancer). Several studies suggest that these aggregation and/or fibril formation processes are often initiated by transient conformational changes of the IDPs prior to protein self-assembly. Interestingly, the pathological molecular processes of these IDPs share multiple common features with those of protein misfolding diseases, such as transmissible spongiform encephalopathy (PrPsc) and AL-amyloidosis (VL-domain of γ-immunoglobulin). This review provides an overview of solution NMR techniques that can help analyse the early and transient events of conformational equilibrium of IDPs and folded proteins.

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.

Lattice model for amyloid peptides: OPEP force field parametrization and applications to the nucleus size of Alzheimer's peptides

Coarse-grained protein lattice models approximate atomistic details and keep the essential interactions. They are, therefore, suitable for capturing generic features of protein folding and amyloid formation at low computational cost. As our aim is to study the critical nucleus sizes of two experimentally well-characterized peptide fragments Aβ16-22 and Aβ37-42 of the full length Aβ1-42 Alzheimer's peptide, it is important that simulations with the lattice model reproduce all-atom simulations. In this study, we present a comprehensive force field parameterization based on the OPEP (Optimized Potential for Efficient protein structure Prediction) force field for an on-lattice protein model, which incorporates explicitly the formation of hydrogen bonds and directions of side-chains. Our bottom-up approach starts with the determination of the best lattice force parameters for the Aβ16-22 dimer by fitting its equilibrium parallel and anti-parallel β-sheet populations to all-atom simulation results. Surprisingly, the calibrated force field is transferable to the trimer of Aβ16-22 and the dimer and trimer of Aβ37-42. Encouraged by this finding, we characterized the free energy landscapes of the two decamers. The dominant structure of the Aβ16-22 decamer matches the microcrystal structure. Pushing the simulations for aggregates between 4-mer and 12-mer suggests a nucleus size for fibril formation of 10 chains. In contrast, the Aβ37-42 decamer is largely disordered with mixed by parallel and antiparallel chains, suggesting that the nucleus size is >10 peptides. Our refined force field coupled to this on-lattice model should provide useful insights into the critical nucleation number associated with neurodegenerative diseases.

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.

Toxicity of serum albumin on microglia upon seeding effect of amyloid peptide

We demonstrate in vitro cross-seeding of bovine serum albumin (BSA) in the presence of Aβ_25-35 and their cytotoxic effects on microglial cells. To investigate the cross-seeding of BSA in the presence of Aβ_25-35 fibrils, we examined how Aβ_25-35 fibrils can function as seeds to trigger and accelerate BSA fibrillogenesis using ThT, intrinsic fluorescence, ANS fluorescence and transmission electron microscopy (TEM). Moreover, the effects of these fibrils on microglial viability were measured using MTT and Annexin V/propidium iodide (PI) staining. Although Aβ_25-35 is toxic against microglia, it acted as seed and affected the aggregation pathway and accelerated the fibrillogenesis of BSA in vitro, resulted in an enhanced cytotoxic effect in comparison with Aβ_25-35 or BSA alone. These observations thought to be helpful to understand the molecular mechanism of enhanced toxicity due to the coexistence of the aggregation prone proteins/peptides,. then cross-seeding effect on microglial cells that may involve in neurodegenerative diseases such as Alzheimer's disease (AD).

Kinetics of protein fibril formation: Methods and mechanisms

Amyloid fibril formation is a self-assembly reaction induced by favourable conformational changes of proteins leading to a stable, structurally organized aggregates. The deposition of stable protein fibrils in organs and tissues results in many diseases which are generally referred as amyloidosis. Though different disease conditions originate from sequentially and structurally different proteins, their fibrillar forms share common structural features. In vitro, fibril structure and kinetic pathway are investigated by using spectroscopic (fluorescence, circular dichroism, crystallography and solid state-NMR) and microscopic techniques. The kinetics of fibril formation is analysed using different mechanisms to understand the microscopic processes involved in the fibrillation reaction. This review discusses the assumptions, mechanisms, and limitations of some of the widely applied kinetic equations. Understanding of these equations would help to quantify the effect of the different microscopic process on the overall fibrillation kinetics which could aid in designing appropriate molecules to intervene in the aggregation process at different stages.

Critical Nucleus Structure and Aggregation Mechanism of the C-terminal Fragment of Copper-Zinc Superoxide Dismutase Protein

The aggregation of the copper-zinc superoxide dismutase (SOD1) protein is linked to familial amyotrophic lateral sclerosis, a progressive neurodegenerative disease. A recent experimental study has shown that the (147)GVIGIAQ(153) SOD1 C-terminal segment not only forms amyloid fibrils in isolation but also accelerates the aggregation of full-length SOD1, while substitution of isoleucine at site 149 by proline blocks its fibril formation. Amyloid formation is a nucleation-polymerization process. In this study, we investigated the oligomerization and the nucleus structure of this heptapeptide. By performing extensive replica-exchange molecular dynamics (REMD) simulations and conventional MD simulations, we found that the GVIGIAQ hexamers can adopt highly ordered bilayer β-sheets and β-barrels. In contrast, substitution of I149 by proline significantly reduces the β-sheet probability and results in the disappearance of bilayer β-sheet structures and the increase of disordered hexamers. We identified mixed parallel-antiparallel bilayer β-sheets in both REMD and conventional MD simulations and provided the conformational transition from the experimentally observed parallel bilayer sheets to the mixed parallel-antiparallel bilayer β-sheets. Our simulations suggest that the critical nucleus consists of six peptide chains and two additional peptide chains strongly stabilize this critical nucleus. The stabilized octamer is able to recruit additional random peptides into the β-sheet. Therefore, our simulations provide insights into the critical nucleus formation and the smallest stable nucleus of the (147)GVIGIAQ(153) peptide.

Comparison of the aggregation of homologous β2-microglobulin variants reveals protein solubility as a key determinant of amyloid formation

The mouse and human β2-microglobulin protein orthologs are 70% identical in sequence and share 88% sequence similarity. These proteins are predicted by various algorithms to have similar aggregation and amyloid propensities. However, whilst human β2m (hβ2m) forms amyloid-like fibrils in denaturing conditions (e.g. pH2.5) in the absence of NaCl, mouse β2m (mβ2m) requires the addition of 0.3M NaCl to cause fibrillation. Here, the factors which give rise to this difference in amyloid propensity are investigated. We utilise structural and mutational analyses, fibril growth kinetics and solubility measurements under a range of pH and salt conditions, to determine why these two proteins have different amyloid propensities. The results show that, although other factors influence the fibril growth kinetics, a striking difference in the solubility of the proteins is a key determinant of the different amyloidogenicity of hβ2m and mβ2m. The relationship between protein solubility and lag time of amyloid formation is not captured by current aggregation or amyloid prediction algorithms, indicating a need to better understand the role of solubility on the lag time of amyloid formation. The results demonstrate the key contribution of protein solubility in determining amyloid propensity and lag time of amyloid formation, highlighting how small differences in protein sequence can have dramatic effects on amyloid formation.

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.

Amyloid Fibril Solubility

It is well established that amyloid fibril solubility is protein specific, but how solubility depends on the interactions between the fibril building blocks is not clear. Here we use a simple protein model and perform Monte Carlo simulations to directly measure the solubility of amyloid fibrils as a function of the interaction between the fibril building blocks. Our simulations confirms that the fibril solubility depends on the fibril thickness and that the relationship between the interactions and the solubility can be described by a simple analytical formula. The results presented in this study reveal general rules how side-chain-side-chain interactions, backbone hydrogen bonding, and temperature affect amyloid fibril solubility, which might prove to be a powerful tool to design protein fibrils with desired solubility and aggregation properties in general.

High-throughput analysis of ultrasonication-forced amyloid fibrillation reveals the mechanism underlying the large fluctuation in the lag time

Amyloid fibrils form in supersaturated solutions of precursor proteins by a nucleation and growth mechanism characterized by a lag time. Although the lag time provides a clue to understanding the complexity of nucleation events, its long period and low reproducibility have been obstacles for exact analysis. Ultrasonication is known to effectively break supersaturation and force fibrillation. By constructing a Handai amyloid burst inducer, which combines a water bath-type ultrasonicator and a microplate reader, we examined the ultrasonication-forced fibrillation of several proteins, with a focus on the fluctuation in the lag time. Amyloid fibrillation of hen egg white lysozyme was examined at pH 2.0 in the presence of 1.0-5.0 M guanidine hydrochloride (GdnHCl), in which the dominant species varied from the native to denatured conformations. Although fibrillation occurred at various concentrations of GdnHCl, the lag time varied largely, with a minimum being observed at ∼3.0 M, the concentration at which GdnHCl-dependent denaturation ended. The coefficient of variation of the lag time did not depend significantly on the GdnHCl concentration and was 2-fold larger than that of the ultrasonication-dependent oxidation of iodide, a simple model reaction. These results suggest that the large fluctuation observed in the lag time for amyloid fibrillation originated from a process associated with a common amyloidogenic intermediate, which may have been a relatively compact denatured conformation. We also suggest that the Handai amyloid burst inducer system will be useful for studying the mechanism of crystallization of proteins because proteins form crystals by the same mechanism as amyloid fibrils under supersaturation.

Simulations of Protein Aggregation: Insights from Atomistic and Coarse-Grained Models

This Perspective highlights recent computational approaches to protein aggregation, from coarse-grained models to atomistic simulations, using the islet amyloid polypeptide (IAPP) as a case study. We review salient open questions where simulations can make an impact, discuss the successes and challenges met by simulations, and explore new directions.

Relationship between the initial rate of protein aggregation and the lag period for amorphous aggregation

Lag period is an inherent characteristic of the kinetic curves registered for protein aggregation. The appearance of a lag period is connected with the nucleation stage and the stages of the formation of folding or unfolding intermediates prone to aggregation (for example, the stage of protein unfolding under stress conditions). Discovering the kinetic regularities essential for elucidation of the protein aggregation mechanism comprises deducing the relationship between the lag period and aggregation rate. Fändrich proposed the following equation connecting the duration of the lag phase (tlag) and the aggregate growth rate (kg) in the amyloid fibrillation: kg=const/tlag. To establish the relationship between the initial rate of protein aggregation (v) and the lag period (t0) in the case of amorphous aggregation, the kinetics of dithithreitol-induced aggregation of holo-α-lactalbumin from bovine milk was studied (0.1M Na-phosphate buffer, pH 6.8; 37°C). The order of aggregation with respect to protein (n) was calculated from the dependence of the initial rate of protein aggregation on the α-lactalbumin concentration (n=5.3). The following equation connecting v and t0 has been proposed: v(1/n)=const/(t0-t0,lim), where t0,lim is the limiting value of t0 at high concentrations of the protein.

Understanding amyloid fibril nucleation and aβ oligomer/drug interactions from computer simulations

Evolution has fine-tuned proteins to accomplish a variety of tasks. Yet, with aging, some proteins assemble into harmful amyloid aggregates associated with neurodegenerative diseases, such as Alzheimer's disease (AD), which presents a complex and costly challenge to our society. Thus, far, drug after drug has failed to slow the progression of AD, characterized by the self-assembly of the 39-43 amino acid β-amyloid (Aβ) protein into extracellular senile plaques that form a cross-β structure. While there is experimental evidence that the Aβ small oligomers are the primary toxic species, standard tools of biology have failed to provide structures of these transient, inhomogeneous assemblies. Despite extensive experimental studies, researchers have not successfully characterized the nucleus ensemble, the starting point for rapid fibril formation. Similarly scientists do not have atomic data to show how the compounds that reduce both fibril formation and toxicity in cells bind to Aβ42 oligomers. In this context, computer simulations are important tools for gaining insights into the self-assembly of amyloid peptides and the molecular mechanism of inhibitors. This Account reviews what analytical models and simulations at different time and length scales tell us about the dynamics, kinetics, and thermodynamics of amyloid fibril formation and, notably, the nucleation process. Though coarse-grained and mesoscopic protein models approximate atomistic details by averaging out unimportant degrees of freedom, they provide generic features of amyloid formation and insights into mechanistic details of the self-assembly process. The thermodynamics and kinetics vary from linear peptides adopting straight β-strands in fibrils to longer peptides adopting in parallel U shaped conformations in fibrils. In addition, these properties change with the balance between electrostatic and hydrophobic interactions and the intrinsic disorder of the system. However, simulations suggest that the critical nucleus size might be on the order of 20 chains under physiological conditions. The transition state might be characterized by a simultaneous change from mixed antiparallel/parallel β-strands with random side-chain packing to the final antiparallel or parallel states with the steric zipper packing of the side chains. Second, we review our current computer-based knowledge of the 3D structures of inhibitors with Aβ42 monomer and oligomers, a prerequisite for developing new drugs against AD. Recent extensive all-atom simulations of Aβ42 dimers with known inhibitors such as the green tea compound epigallocatechin-3-gallate and 1,4-naphthoquinon-2-yl-l-tryptophan provide a spectrum of initial Aβ42/inhibitor structures useful for screening and drug design. We conclude by discussing future directions that may offer opportunities to fully understand nucleation and further AD drug development.

New method for determining size of critical nucleus of fibril formation of polypeptide chains

A new method for determining the size of critical nucleus of fibril formation of polypeptide chains is proposed. Based on the hypothesis that the fibril grows by addition of a nascent peptide to the preformed template, the nucleus size N(c) is defined as the number of forming template peptides above which the time to add a new monomer becomes independent of the template size. Using lattice models one can show that our method and the standard method which is based on calculation of the free energy, provide the same result for N(c).

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.

Selective molecular recognition in amyloid growth and transmission and cross-species barriers

Mutual conformational selection and population shift followed by minor induced-fit optimization is the key mechanism in biomolecular recognition, and monomers and small oligomers binding to amyloid seeds in fibril growth is a molecular recognition event. Here, we describe amyloid aggregation, preferred species, cross-species barriers and transmission within the broad framework of molecular recognition. Cross-seeding of amyloid species is governed by conformational selection of compatible (complementary) states. If the dominant conformations of two species are similar, they can cross-seed each other; on the other hand, if they are sufficiently different, they will grow into different fibrils, reflecting species barriers. Such a scenario has recently been observed for the tau protein, which has four repeats. While a construct consisting of repeats 1, 3 and 4 can serve as a seed for the entire four-repeat tau segment, the inverse does not hold. On the other hand, the tau protein repeats with the characteristic U-turn shape can cross-seed Alzheimer's amyloid β and, similarly, the islet amyloid polypeptide. Within this framework, we suggest that the so-called "central dogma" of amyloid formation, where aggregation takes place through nonspecific backbone hydrogen bonding interactions, which are common to all peptides and proteins, is a simple reflection of the heterogeneous, polymorphic free-energy landscape of amyloid species. Here, we review available data and make some propositions addressing this key problem. In particular, we argue that recent theoretical and experimental observations support the key role of selective molecular recognition in amyloidosis and in determining cross-species barriers and transmission.

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.

Protein aggregation: mechanisms and functional consequences

Understanding the mechanisms underlying protein misfolding and aggregation has become a central issue in biology and medicine. Compelling evidence show that the formation of amyloid aggregates has a negative impact in cell function and is behind the most prevalent human degenerative disorders, including Alzheimer's Parkinson's and Huntington's diseases or type 2 diabetes. Surprisingly, the same type of macromolecular assembly is used for specialized functions by different organisms, from bacteria to human. Here we address the conformational properties of these aggregates, their formation pathways, their role in human diseases, their functional properties and how bioinformatics tools might be of help to study these protein assemblies.

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.