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

Stability and deformation of biomolecular condensates under the action of shear flow

Biomolecular condensates play a key role in cytoplasmic compartmentalization and cell functioning. Despite extensive research on the physico-chemical, thermodynamic, or crowding aspects of the formation and stabilization of the condensates, one less studied feature is the role of external perturbative fluid flow. In fact, in living cells, shear stress may arise from streaming or active transport processes. Here, we investigate how biomolecular condensates are deformed under different types of shear flows. We first model Couette flow perturbations via two-way coupling between the condensate dynamics and fluid flow by deploying Lattice Boltzmann Molecular Dynamics. We then show that a simplified approach where the shear flow acts as a static perturbation (one-way coupling) reproduces the main features of the condensate deformation and dynamics as a function of the shear rate. With this approach, which can be easily implemented in molecular dynamics simulations, we analyze the behavior of biomolecular condensates described through residue-based coarse-grained models, including intrinsically disordered proteins and protein/RNA mixtures. At lower shear rates, the fluid triggers the deformation of the condensate (spherical to oblated object), while at higher shear rates, it becomes extremely deformed (oblated or elongated object). At very high shear rates, the condensates are fragmented. We also compare how condensates of different sizes and composition respond to shear perturbation, and how their internal structure is altered by external flow. Finally, we consider the Poiseuille flow that realistically models the behavior in microfluidic devices in order to suggest potential experimental designs for investigating fluid perturbations in vitro.

Genetic Algorithm for Automated Parameterization of Network Hamiltonian Models of Amyloid Fibril Formation

The time scales of long-time atomistic molecular dynamics simulations are typically reported in microseconds, while the time scales for experiments studying the kinetics of amyloid fibril formation are typically reported in minutes or hours. This time scale deficit of roughly 9 orders of magnitude presents a major challenge in the design of computer simulation methods for studying protein aggregation events. Coarse-grained molecular simulations offer a computationally tractable path forward for exploring the molecular mechanism driving the formation of these structures, which are implicated in diseases such as Alzheimer's, Parkinson's, and type-II diabetes. Network Hamiltonian models of aggregation are centered around a Hamiltonian function that returns the total energy of a system of aggregating proteins, given the graph structure of the system as an input. In the graph, or network, representation of the system, each protein molecule is represented as a node, and noncovalent bonds between proteins are represented as edges. The parameter, i.e., a set of coefficients that determine the degree to which each topological degree of freedom is favored or disfavored, must be determined for each network Hamiltonian model, and is a well-known technical challenge. The methodology is first demonstrated by beginning with an initial set of randomly parametrized models of low fibril fraction (<5% fibrillar), and evolving to subsequent generations of models, ultimately leading to high fibril fraction models (>70% fibrillar). The methodology is also demonstrated by applying it to optimizing previously published network Hamiltonian models for the 5 key amyloid fibril topologies that have been reported in the Protein Data Bank (PDB). The models generated by the AI produced fibril fractions that surpass previously published fibril fractions in 3 of 5 cases, including the most naturally abundant amyloid fibril topology, the 1,2 2-ribbon, which features a steric zipper. The authors also aim to encourage more widespread use of the network Hamiltonian methodology for fitting a wide variety of self-assembling systems by releasing a free open-source implementation of the genetic algorithm introduced here.

Dynamics and Structures of Amyloid Aggregates under Fluid Flows

In this work, we investigate how fluid flows impact the aggregation mechanisms of Aβ40 proteins and Aβ16-22 peptides and mechanically perturb their (pre)fibrillar aggregates. We exploit the OPEP coarse-grained model for proteins and the Lattice Boltzmann Molecular Dynamics technique. We show that beyond a critical shear rate, amyloid aggregation speeds up in Couette flow because of the shorter collisions times between aggregates, following a transition from diffusion limited to advection dominated dynamics. We also characterize the mechanical deformation of (pre)fibrillar states due to the fluid flows (Couette and Poiseuille), confirming the capability of (pre)fibrils to form pathological loop-like structures as detected in experiments. Our findings can be of relevance for microfluidic applications and for understanding aggregation in the interstitial brain space.

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

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

Evolution of large Aβ16-22 aggregates at atomic details and potential of mean force associated to peptide unbinding and fragmentation events

Atomic characterization of large nonfibrillar aggregates of amyloid polypeptides cannot be determined by experimental means. Starting from β-rich aggregates of Y and elongated topologies predicted by coarse-grained simulations and consisting of more than 100 Aβ16-22 peptides, we performed atomistic molecular dynamics (MD), replica exchange with solute scaling (REST2), and umbrella sampling simulations using the CHARMM36m force field in explicit solvent. Here, we explored the dynamics within 3 μs, the free energy landscape, and the potential of mean force associated with either the unbinding of one single peptide in different configurations within the aggregate or fragmentation events of a large number of peptides. Within the time scale of MD and REST2, we find that the aggregates experience slow global conformational plasticity, and remain essentially random coil though we observe slow beta-strand structuring with a dominance of antiparallel beta-sheets over parallel beta-sheets. Enhanced REST2 simulation is able to capture fragmentation events, and the free energy of fragmentation of a large block of peptides is found to be similar to the free energy associated with fibril depolymerization by one chain for longer Aβ sequences.

Optimized OPEP Force Field for Simulation of Crowded Protein Solutions

Macromolecular crowding has profound effects on the mobility of proteins, with strong implications on the rates of intracellular processes. To describe the dynamics of crowded environments, detailed molecular models are needed, capturing the structures and interactions arising in the crowded system. In this work, we present OPEPv7, which is a coarse-grained force field at amino-acid resolution, suited for rigid-body simulations of the structure and dynamics of crowded solutions formed by globular proteins. Using the OPEP protein model as a starting point, we have refined the intermolecular interactions to match the experimentally observed dynamical slowdown caused by crowding. The resulting force field successfully reproduces the diffusion slowdown in homogeneous and heterogeneous protein solutions at different crowding conditions. Coupled with the lattice Boltzmann technique, it allows the study of dynamical phenomena in protein assemblies and opens the way for the in silico rheology of protein solutions.

Metastable alpha-rich and beta-rich conformations of small Aβ42 peptide oligomers

Probing the structures of amyloid-β (Aβ) peptides in the early steps of aggregation is extremely difficult experimentally and computationally. Yet, this knowledge is extremely important as small oligomers are the most toxic species. Experiments and simulations on Aβ42 monomer point to random coil conformations with either transient helical or β-strand content. Our current conformational description of small Aβ42 oligomers is funneled toward amorphous aggregates with some β-sheet content and rare high energy states with well-ordered assemblies of β-sheets. In this study, we emphasize another view based on metastable α-helix bundle oligomers spanning the C-terminal residues, which are predicted by the machine-learning AlphaFold2 method and supported indirectly by low-resolution experimental data on many amyloid polypeptides. This finding has consequences in developing novel chemical tools and to design potential therapies to reduce aggregation and toxicity.

An operative framework to model mucus clearance in silico by coupling cilia motion with the liquid environment

Mucociliary clearance is the first defense mechanism of the respiratory tract against inhaled particles. This mechanism is based on the collective beating motion of cilia at the surface of epithelial cells. Impaired clearance, either caused by malfunctioning or absent cilia, or mucus defects, is a symptom of many respiratory diseases. Here, by exploiting the lattice Boltzmann particle dynamics technique, we develop a model to simulate the dynamics of multiciliated cells in a two-layer fluid. First, we tuned our model to reproduce the characteristic length- and time-scales of the cilia beating. We then check for the emergence of the metachronal wave as a consequence of hydrodynamic mediated correlations between beating cilia. Finally, we tune the viscosity of the top fluid layer to simulate the mucus flow upon cilia beating, and evaluate the pushing efficiency of a carpet of cilia. With this work, we build a realistic framework that can be used to explore several important physiological aspects of mucociliary clearance.

Self-Assembly of Amyloid-Beta (Aβ) Peptides from Solution to Near In Vivo Conditions

Understanding the atomistic resolution changes during the self-assembly of amyloid peptides or proteins is important to develop compounds or conditions to alter the aggregation pathways and suppress the toxicity and potentially aid in the development of drugs. However, the complexity of protein aggregation and the transient order/disorder of oligomers along the pathways to fibril are very challenging. In this Perspective, we discuss computational studies of amyloid polypeptides carried out under various conditions, including conditions closely mimicking in vivo and point out the challenges in obtaining physiologically relevant results, focusing mainly on the amyloid-beta Aβ peptides.

Nanoscale Infrared Spectroscopy Identifies Parallel to Antiparallel β-Sheet Transformation of Aβ Fibrils

Spontaneous aggregation of amyloid beta (Aβ) proteins leading to the formation of oligomers and eventually into fibrils has been identified as a key pathological signature of Alzheimer's disease. The structure of late-stage aggregates have been studied in depth by conventional structural biology techniques, including nuclear magnetic resonance, X-ray crystallography, and infrared spectroscopy; however, the structure of early-stage aggregates is less known due to their transient nature. As a result, the structural evolution of amyloid aggregates from early oligomers to mature fibrils is still not fully understood. Here, we have applied atomic force microscopy-infrared nanospectroscopy to investigate the aggregation of Aβ 16-22, which spans the amyloidogenic core of the Aβ peptide. Our results demonstrate that Aβ 16-22 involves a structural transition from oligomers with parallel β-sheets to antiparallel fibrils through disordered and possibly helical intermediate fibril structures, contrary to the known aggregation pathway of full-length Aβ.

Amyloidogenesis: What Do We Know So Far?

The study of protein aggregation, and amyloidosis in particular, has gained considerable interest in recent times. Several neurodegenerative diseases, such as Alzheimer's (AD) and Parkinson's (PD) show a characteristic buildup of proteinaceous aggregates in several organs, especially the brain. Despite the enormous upsurge in research articles in this arena, it would not be incorrect to say that we still lack a crystal-clear idea surrounding these notorious aggregates. In this review, we attempt to present a holistic picture on protein aggregation and amyloids in particular. Using a chronological order of discoveries, we present the case of amyloids right from the onset of their discovery, various biophysical techniques, including analysis of the structure, the mechanisms and kinetics of the formation of amyloids. We have discussed important questions on whether aggregation and amyloidosis are restricted to a subset of specific proteins or more broadly influenced by the biophysiochemical and cellular environment. The therapeutic strategies and the significant failure rate of drugs in clinical trials pertaining to these neurodegenerative diseases have been also discussed at length. At a time when the COVID-19 pandemic has hit the globe hard, the review also discusses the plausibility of the far-reaching consequences posed by the virus, such as triggering early onset of amyloidosis. Finally, the application(s) of amyloids as useful biomaterials has also been discussed briefly in this review.

Kinetic Mechanism of Amyloid-β-(16-22) Peptide Fibrillation

The kinetic mechanism of amyloid fibril formation by a peptide fragment containing seven residues of the amyloid-β protein Aβ-(16-22) was investigated. We found that the N- and C-terminal unprotected Aβ-(16-22), containing no aggregation nuclei, showed rapid fibrillation within seconds to minutes in a neutral aqueous buffer solution. The fibrillation kinetics were well described by the nucleation-elongation model, suggesting that primary nucleation was the rate-limiting step. On the basis of both experimental and theoretical analyses, the aggregated nucleus was estimated to be composed of 6-7 peptide molecules, wherein the two β-sheets were associated with their hydrophobic surfaces. Thin fibers with widths of 10-20 nm were formed, which increased their length and thickness, attaining a width of >20 nm over several tens of minutes, probably owing to the lateral association of the fibers. Electrostatic and hydrophobic interactions play important roles in aggregation. These results provide a basis for understanding the fibrillation of short peptides.

Development of a Hybrid-Resolution Force Field for Peptide Self-Assembly Simulations: Optimizing Peptide-Peptide and Peptide-Solvent Interactions

Atomic descriptions of peptide self-assembly are crucial to an understanding of disease-related peptide aggregation and the design of peptide-assembled materials. Obtaining these descriptions through computer simulation is challenging because current force fields, which were not designed for this process and are often unable to describe correctly peptide self-assembly behavior and the sequence dependence. Here, we developed a framework using dipeptide aggregation as a model system to improve force fields for simulations of self-assembly. Aggregation-related structural properties were designed and used to guide the optimization of peptide-peptide and peptide-solvent interactions. With this framework, we developed a self-assembly force field, termed PACE-ASM, by reoptimizing a hybrid-resolution force field that was originally developed for folding simulation. With its applicability in folding simulations, the new PACE was used to simulate the self-assembly of two disease-related short peptides, Aβ_16-21 and PHF6, into β-sheet-rich cross-β amyloids. These simulations reproduced the crystal structures of Aβ_16-21 and PHF6 amyloids at near-atomic resolution and captured the difference in packing orientations between the two sequences, a task which is challenging even with all-atom force fields. Apart from cross-β amyloids, the self-assembly of emerging helix-rich cross-α amyloids by another peptide PSMα3 can also be correctly described with the new PACE, manifesting the versatility of the force field. We demonstrated that the ability of the PACE-ASM to model peptide self-assembly is based largely on its improved description of peptide-peptide and peptide-solvent interactions. This was achieved with our optimization framework that can readily identify and address the deficiency in describing these interactions.

Computational models for studying physical instabilities in high concentration biotherapeutic formulations

Computational prediction of the behavior of concentrated protein solutions is particularly advantageous in early development stages of biotherapeutics when material availability is limited and a large set of formulation conditions needs to be explored. This review provides an overview of the different computational paradigms that have been successfully used in modeling undesirable physical behaviors of protein solutions with a particular emphasis on high-concentration drug formulations. This includes models ranging from all-atom simulations, coarse-grained representations to macro-scale mathematical descriptions used to study physical instability phenomena of protein solutions such as aggregation, elevated viscosity, and phase separation. These models are compared and summarized in the context of the physical processes and their underlying assumptions and limitations. A detailed analysis is also given for identifying protein interaction processes that are explicitly or implicitly considered in the different modeling approaches and particularly their relations to various formulation parameters. Lastly, many of the shortcomings of existing computational models are discussed, providing perspectives and possible directions toward an efficient computational framework for designing effective protein formulations.

Anatomy and Formation Mechanisms of Early Amyloid-β Oligomers with Lateral Branching: Graph Network Analysis on Large-Scale Simulations

Oligomeric amyloid-β aggregates (AβOs) effectively trigger Alzheimer's disease-related toxicity, generating great interest in understanding their structures and formation mechanisms. However, AβOs are heterogeneous and transient, making their structure and formation difficult to study. Here, we performed graph network analysis of tens of microsecond massive simulations of early amyloid-β (Aβ) aggregations at near-atomic resolution to characterize AβO structures with sizes up to 20-mers. We found that AβOs exhibit highly curvilinear, irregular shapes with occasional lateral branches, consistent with recent cryo-electron tomography experiments. We also found that Aβ40 oligomers were more likely to develop branches than Aβ42 oligomers, explaining an experimental observation that only Aβ40 was trapped in network-like aggregates and exhibited slower fibrillization kinetics. Moreover, AβO architecture dissection revealed that their curvilinear appearance is related to the local packing geometries of neighboring peptides and that Aβ40's greater branching ability originates from specific C-terminal interactions at branching interfaces. Finally, we demonstrate that whether Aβ oligomerization causes oligomers to elongate or to branch depends on the sizes and shapes of colliding aggregates. Collectively, this study provides bottom-up structural information for understanding early Aβ aggregation and AβO toxicity.

Graph network analysis on large-scale simulations uncovers the differential branching behaviours of large Aβ40 and Aβ42 oligomers.

Computational Models for the Study of Protein Aggregation

Protein aggregation has been studied by many groups around the world for many years because it can be the cause of a number of neurodegenerative diseases that have no effective treatment. Obtaining the structure of related fibrils and toxic oligomers, as well as describing the pathways and main factors that govern the self-organization process, is of paramount importance, but it is also very difficult. To solve this problem, experimental and computational methods are often combined to get the most out of each method. The effectiveness of the computational approach largely depends on the construction of a reasonable molecular model. Here we discussed different versions of the four most popular all-atom force fields AMBER, CHARMM, GROMOS, and OPLS, which have been developed for folded and intrinsically disordered proteins, or both. Continuous and discrete coarse-grained models, which were mainly used to study the kinetics of aggregation, are also summarized.

Computer Simulations Aimed at Exploring Protein Aggregation and Dissociation

Protein aggregation can lead to well-defined structures that are functional, but is also the cause of the death of neuron cells in many neurodegenerative diseases. The complexity of the molecular events involved in the aggregation kinetics of amyloid proteins and the transient and heterogeneous characters of all oligomers prevent high-resolution structural experiments. As a result, computer simulations have been used to determine the atomic structures of amyloid proteins at different association stages as well as to understand fibril dissociation. In this chapter, we first review the current computer simulation methods used for aggregation with some atomistic and coarse-grained results aimed at better characterizing the early formed oligomers and amyloid fibril formation. Then we present the applications of non-equilibrium molecular dynamics simulations to comprehend the dissociation of protein assemblies.

Dynamics of Amyloid Formation from Simplified Representation to Atomistic Simulations

Amyloid fibril formation is an intrinsic property of short peptides, non-disease proteins, and proteins associated with neurodegenerative diseases. Aggregates of the Aβ and tau proteins, the α-synuclein protein, and the prion protein are observed in the brain of Alzheimer's, Parkinson's, and prion disease patients, respectively. Due to the transient short-range and long-range interactions of all species and their high aggregation propensities, the conformational ensemble of these devastating proteins, the exception being for the monomeric prion protein, remains elusive by standard structural biology methods in bulk solution and in lipid membranes. To overcome these limitations, an increasing number of simulations using different sampling methods and protein models have been performed. In this chapter, we first review our main contributions to the field of amyloid protein simulations aimed at understanding the early aggregation steps of short linear amyloid peptides, the conformational ensemble of the Aβ40/42 dimers in bulk solution, and the stability of Aβ aggregates in lipid membrane models. Then we focus on our studies on the interactions of amyloid peptides/inhibitors to prevent aggregation, and long amyloid sequences, including new results on a monomeric tau construct.

Exposure of Von Willebrand Factor Cleavage Site in A1A2A3-Fragment under Extreme Hydrodynamic Shear

Von Willebrand Factor (vWf) is a giant multimeric extracellular blood plasma involved in hemostasis. In this work we present multi-scale simulations of its three-domains fragment A1A2A3. These three domains are essential for the functional regulation of vWf. Namely the A2 domain hosts the site where the protease ADAMTS13 cleavages the multimeric vWf allowing for its length control that prevents thrombotic conditions. The exposure of the cleavage site follows the elongation/unfolding of the domain that is caused by an increased shear stress in blood. By deploying Lattice Boltzmann molecular dynamics simulations based on the OPEP coarse-grained model for proteins, we investigated at molecular level the unfolding of the A2 domain under the action of a perturbing shear flow. We described the structural steps of this unfolding that mainly concerns the β-strand structures of the domain, and we compared the process occurring under shear with that produced by the action of a directional pulling force, a typical condition of single molecule experiments. We observe, that under the action of shear flow, the competition among the elongational and rotational components of the fluid field leads to a complex behaviour of the domain, where elongated structures can be followed by partially collapsed melted globule structures with a very different degree of exposure of the cleavage site. Our simulations pose the base for the development of a multi-scale in-silico description of vWf dynamics and functionality in physiological conditions, including high resolution details for molecular relevant events, e.g., the binding to platelets and collagen during coagulation or thrombosis.

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

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

Acceleration of α-synuclein fibril formation and associated cytotoxicity stimulated by silica nanoparticles as a model of neurodegenerative diseases

A wide range of biophysical and theoretical analysis were employed to explore the formation of (α-syn) amyloid fibril formation as a model of Parkinson's disease in the presence of silica oxide nanoparticles (SiO₂ NPs). Also, different cellular and molecular assays such as MTT, LDH, caspase, ROS, and qPCR were performed to reveal the α-syn amyloid fibrils-associated cytotoxicity against SH-SY5Y cells. Fluorescence measurements showed that SiO₂ NPs accelerate the α-syn aggregation and exposure of hydrophobic moieties. Congo red absorbance, circular dichroism (CD), and transmission electron microscopy (TEM) analysis depicted the SiO₂ NPs accelerated the formation of α-syn amyloid fibrils. Molecular docking study showed that SiO₂ clusters preferably bind to the N-terminal of α-syn as the helix folding site. We also realized that SiO₂ NPs increase the cytotoxicity of α-syn amyloid fibrils through a significant decrease in cell viability, increase in membrane leakage, activation of caspase-9 and -3, elevation of ROS, and increase in the ratio of Bax/Bcl2 mRNA. The cellular assay indicated that α-syn amyloid fibrils formed in the presence of SiO₂ NPs induce their cytotoxic effects through the mitochondrial-mediated intrinsic apoptosis pathway. We concluded that these data may reveal some adverse effects of NPs on the progression of Parkinson's disease.

Amyloid aggregation simulations: challenges, advances and perspectives

In amyloid aggregation diseases soluble proteins coalesce into a wide array of undesirable structures, ranging through oligomers and prefibrillar assemblies to highly ordered amyloid fibrils and plaques. Explicit-solvent all-atom molecular dynamics (MD) simulations of amyloid aggregation have been performed for almost 20 years, revealing valuable information about this phenomenon. However, these simulations are challenged by three main problems. Firstly, current force fields modeling amyloid aggregation are insufficiently accurate. Secondly, the protein concentrations in MD simulations are usually orders of magnitude higher than those used in vitro or found in vivo, which has direct consequences on the aggregates that form. Finally, the third problem is the well-known time-scale limit of MD simulations. In this review I highlight recent approaches to overcome these three limitations.

Latent Models of Molecular Dynamics Data: Automatic Order Parameter Generation for Peptide Fibrillization

Variational autoencoders are artificial neural networks with the capability to reduce highly dimensional sets of data to smaller dimensional, latent representations. In this work, these models are applied to molecular dynamics simulations of the self-assembly of coarse-grained peptides to obtain a singled-valued order parameter for amyloid aggregation. This automatically learned order parameter is constructed by time-averaging the latent parametrizations of internal coordinate representations and compared to the nematic order parameter which is commonly used to study ordering of similar systems in literature. It is found that the latent space value provides more tailored insight into the aggregation mechanism's details, correctly identifying fibril formation in instances where the nematic order parameter fails to do so. A means is provided by which the latent space value can be analyzed so that the major contributing internal coordinates are identified, allowing for a direct interpretation of the latent space order parameter in terms of the behavior of the system. The latent model is found to be an effective and convenient way of representing the data from the dynamic ensemble and provides a means of reducing the dimensionality of a system whose scale exceeds molecular systems so-far considered with similar tools. This bypasses a need for researcher speculation on what elements of a system best contribute to summarizing major transitions and suggests latent models are effective and insightful when applied to large systems with a diversity of complex behaviors.

Structures of the intrinsically disordered Aβ, tau and α-synuclein proteins in aqueous solution from computer simulations

Intrinsically disordered proteins (IDPs) play many biological roles in the human proteome ranging from vesicular transport, signal transduction to neurodegenerative diseases. The Aβ and tau proteins, and the α-synuclein protein, key players in Alzheimer's and Parkinson's diseases, respectively are fully disordered at the monomer level. The structural heterogeneity of the monomeric and oligomeric states and the high self-assembly propensity of these three IDPs have precluded experimental structural determination. Simulations have been used to determine the atomic structures of these IDPs. In this article, we review recent computer models to capture the equilibrium ensemble of Aβ, tau and α-synuclein proteins at different association steps in aqueous solution and present new results of the PEP-FOLD framework on α-synuclein monomer.

Aggregation of disease-related peptides

Protein misfolding and aggregation of amyloid proteins is the fundamental cause of more than 20 diseases. Molecular mechanisms of the self-assembly and the formation of the toxic aggregates are still elusive. Computer simulations have been intensively used to study the aggregation of amyloid peptides of various amino acid lengths related to neurodegenerative diseases. We review atomistic and coarse-grained simulations of short amyloid peptides aimed at determining their transient oligomeric structures and the early and late aggregation steps.

Network-Based Classification and Modeling of Amyloid Fibrils

Amyloid fibrils are locally ordered protein aggregates that self-assemble under a variety of physiological and in vitro conditions. Their formation is of fundamental interest as a physical chemistry problem and plays a central role in Alzheimer's disease, Type II diabetes, and other human diseases. As the number of known amyloid fibril structures has grown, the need has arisen for a nomenclature for describing and classifying fibril types, as well as a theoretical description of the physics that gives rise to the self-assembly of these structures. Here, we introduce a systematic nomenclature and coarse-graining methodology for describing the topology of fibrils and other protein aggregates, along with a computational methodology for simulating protein aggregation. Both have mathematical underpinnings in graph theory and statistical mechanics and are consistent with available experimental data on the fibril structure and aggregation kinetics. Our graph representation of the fibril topology enables us to define a network Hamiltonian based on connectivity patterns among monomers rather than detailed intermolecular interactions, greatly speeding up the simulation of large ensembles. Our simulation strategy is capable of recapitulating the formation of all currently known amyloid fibril topologies found in the Protein Data Bank, as well as the formation kinetics of fibrils and oligomers.