Primary Nucleation Kinetics of Short Fibril-Forming Amyloidogenic Peptides

Characterizing the Sequence Landscape of Peptide Fibrillization with a Bottom-Up Coarse-Grained Model

Molecular insight into amyloid aggregation is crucial for understanding the details of protein fibril nucleation and growth, which play a significant role in a wide range of proteinopathies. The length and time scales for fibrillization make its computational study an intrinsically multiscale problem, necessitating the use of coarse-grained modeling. A wide variety of coarse-grained models for peptides have been proposed, often parametrized with a combination of top-down and bottom-up approaches. Here, we present a predictive, sequence-transferable bottom-up coarse-grained model, systematically developed using only information from atomistic simulations by applying an extended-ensemble relative entropy minimization technique. The resulting model is capable of accurately recovering conformational properties of peptides constructed from a reduced alphabet of amino acids, of predicting secondary structures of isolated and interacting peptides from their sequences alone, and of simulating aggregation of peptides that have been experimentally characterized as amyloidogenic. Finally, we couple such coarse-grained simulations with a genetic algorithm to characterize the sequence space of the reduced alphabet and identify features of sequences for which ordered fibrillar states are both thermodynamically favorable and kinetically accessible.

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

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

Antibody Aggregation: A Problem Within the Biopharmaceutical Industry and Its Role in AL Amyloidosis Disease

Due to the large size and rapid growth of the global therapeutic antibody market, there is major interest in understanding the aggregation of protein products as it can compromise efficacy, concentration, and safety. Various production and storage conditions have been identified as capable of inducing aggregation of polyclonal and monoclonal antibody (mAb) therapies such as low pH, freezing, light exposure, lyophilisation and increased ionic strength. The addition of stabilising excipients to these therapeutics helps to combat the formation of aggregates with future aggregation inhibition mechanisms involving the introduction of point mutations and glycoengineering within aggregation prone regions (APRs). Antibody aggregation also plays an integral role in the pathogenesis of a condition known as amyloid light chain (AL) amyloidosis which is characterised by the production of improperly folded and amyloidogenic immunoglobulin light chains (LCs). Current diagnostic tools rely heavily on histological staining with their future moving towards amyloid component identification and proteomic analysis. For many years, treatment options designed for multiple myeloma (MM) have been applied to AL amyloidosis patients by depleting plasma cell numbers. More recently, treatment strategies more specific to this condition have been developed with many designed to recognize amyloid fibrils and trigger their degradation without causing systemic plasma cell cytotoxicity. Amyloid fibrils in AL disease and aggregates in antibody therapeutics are both formed through the oligomerisation of misfolded / modified proteins attempting to reach a thermodynamically stable, free energy minimum that is lower than the respective monomers themselves. Although the final morphologies are different, by understanding the principles underlying such aggregation, we expect to find common insights that may contribute to the development of new and effective methods of antibody aggregation and/or amyloidosis management. We envision that this area of research will continue to be very relevant in both industry and clinical settings.

From Fundamental Amyloid Protein Self-Assembly to Development of Bioplastics

Proteins can self-assemble into a range of nanostructures as a result of molecular interactions. Amyloid nanofibrils, as one of them, were first discovered with regard to the relevance of neurodegenerative diseases but now have been exploited as building blocks to generate multiscale materials with designed functions for versatile applications. This review interconnects the mechanism of amyloid fibrillation, the current approaches to synthesizing amyloid protein-based materials, and the application in bioplastic development. We focus on the fundamental structures of self-assembled amyloid fibrils and how external factors can affect protein aggregation to optimize the process. Protein self-assembly is essentially the autonomous congregation of smaller protein units into larger, organized structures. Since the properties of the self-assembly can be manipulated by changing intrinsic factors and external conditions, protein self-assembly serves as an excellent building block for bioplastic development. Building on these principles, general processing methods and pathways from raw protein sources to mature state materials are proposed, providing a guide for the development of large-scale production. Additionally, this review discusses the diverse properties of protein-based amyloid nanofibrils and how they can be utilized as bioplastics. The economic feasibility of the protein bioplastics is also compared to conventional plastics in large-scale production scenarios, supporting their potential as sustainable bioplastics for future applications.

Exploring the Barriers in the Aggregation of a Hexadecameric Human Prion Peptide through the Markov State Model

The prefibrillar aggregation kinetics of prion peptides are still an enigma. In this perspective, we employ atomistic molecular dynamics (MD) simulations of the shortest human prion peptide (HPP) (127GYMLGS132) at various temperatures and peptide concentrations and apply the Markov state model to determine the various intermediates and lag phases. Our results reveal that the natural mechanism of prion peptide self-assembly in the aqueous phase is impeded by two significant kinetic barriers with oligomer sizes of 6-9 and 12-13 peptides, respectively. The first one is the aggregation of unstructured lower-order oligomers, and the second is fibril nucleation, which impedes the further growth of prion aggregates. Among these two activation barriers, the second one is found to be dominant irrespective of the increase in temperature and peptide concentration. These lag phases are captured in all three different force-field parameters, namely, GROMOS-54a7, AMBER-99SB-ILDN, and CHARMMS 36m, at different concentrations. The GROMOS-54a7 and AMBER-99SB-ILDN force fields showed a comparatively higher percentage of β-sheet formation in the metastable aggregate that evolved during the aggregation process. In contrast, the CHARMM-36m force field showed mostly coil or turn conformations. The addition of a novel catecholamine derivative (naphthoquinone dopamine (NQDA)) arrests the aggregation process between the lag phases by increasing the activation barrier for the Lag1 and Lag2 phases in all of the force fields, which further validates the existence of these lag phases. The preferential binding of NQDA with the peptides increases the hydration of peptides and eventually disrupts the organized morphology of prefibrillar aggregates. It reduces the dimer dissociation energy by -24.34 kJ/mol.

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.

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.

Conformational entropy limits the transition from nucleation to elongation in amyloid aggregation

The formation of β-sheet rich amyloid fibrils in Alzheimer's disease and other neurodegenerative disorders is limited by a slow nucleation event. To understand the initial formation of β-sheets from disordered peptides, we used all-atom simulations to parameterize a lattice model that treats each amino acid as a binary variable with β and non-β states. We show that translational and conformational entropy give the nascent β-sheet an anisotropic surface tension which can be used to describe the nucleus with two-dimensional Classical Nucleation Theory. Since translational entropy depends on concentration, the aspect ratio of the critical β-sheet changes with protein concentration. Our model explains the transition from the nucleation phase to elongation as the point where the β-sheet core becomes large enough to overcome the conformational entropy cost to straighten the terminal molecule. At this point the β-strands in the nucleus spontaneously elongate, which results in a larger binding surface to capture new molecules. These results suggest that nucleation is relatively insensitive to sequence differences in co-aggregation experiments because the nucleus only involves a small portion of the peptide.

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

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

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.

Diverse Aggregation Kinetics Predicted by a Coarse-Grained Peptide Model

Protein and peptide aggregation is a ubiquitous phenomenon with implications in medicine, pharmaceutical industry, and materials science. An important issue in peptide aggregation is the molecular mechanism of aggregate nucleation and growth. In many experimental studies, sigmoidal kinetics curves show a clear lag phase ascribed to nucleation; however, experimental studies also show downhill kinetics curves, where the monomers decay continuously and no lag phase can be seen. In this work, we study peptide aggregation kinetics using a coarse-grained implicit solvent model introduced in our previous work. Our simulations explore the hypothesis that the interplay between interchain attraction and intrachain bending stiffness controls the aggregation kinetics and transient aggregate morphologies. Indeed, our model reproduces the aggregation modes seen in experiment: no observed aggregation, nucleated aggregation, and rapid downhill aggregation. We find that the interaction strength is the primary parameter determining the aggregation mode, whereas the stiffness is a secondary parameter modulating the transient morphologies and aggregation rates: more attractive and stiff chains aggregate more rapidly and the transient morphologies are more ordered. We also explore the effects of the initial monomer concentration and the chain length. As the concentration decreases, the aggregation mode shifts from downhill to nucleated and no-aggregation. This concentration effect is in line with an experimental observation that the transition between downhill and nucleated kinetics is concentration-dependent. We find that longer peptides can aggregate at conditions where short peptides do not aggregate at all. It supports an experimental observation that the elongation of a homopeptide, e.g., polyglutamine, can increase the aggregation propensity.

Defining the Neuropathological Aggresome across in Silico, in Vitro, and ex Vivo Experiments

The loss of proteostasis over the life course is associated with a wide range of debilitating degenerative diseases and is a central hallmark of human aging. When left unchecked, proteins that are intrinsically disordered can pathologically aggregate into highly ordered fibrils, plaques, and tangles (termed amyloids), which are associated with countless disorders such as Alzheimer's disease, Parkinson's disease, type II diabetes, cancer, and even certain viral infections. However, despite significant advances in protein folding and solution biophysics techniques, determining the molecular cause of these conditions in humans has remained elusive. This has been due, in part, to recent discoveries showing that soluble protein oligomers, not insoluble fibrils or plaques, drive the majority of pathological processes. This has subsequently led researchers to focus instead on heterogeneous and often promiscuous protein oligomers. Unfortunately, significant gaps remain in how to prepare, model, experimentally corroborate, and extract amyloid oligomers relevant to human disease in a systematic manner. This Review will report on each of these techniques and their successes and shortcomings in an attempt to standardize comparisons between protein oligomers across disciplines, especially in the context of neurodegeneration. By standardizing multiple techniques and identifying their common overlap, a clearer picture of the soluble neuropathological aggresome can be constructed and used as a baseline for studying human disease and aging.

Supramolecular Bait to Trigger Non-Equilibrium Co-Assembly and Clearance of Aβ42

In living systems, non-equilibrium states that control the assembly-disassembly of cellular components underlie the gradual complexification of life, whereas in nonliving systems, most molecules follow the laws of thermodynamic equilibrium to sustain dynamic consistency. Little is known about the roles of non-equilibrium states of interactions between supramolecules in living systems. Here, a non-equilibrium state of interaction between supramolecular lipopolysaccharide (LPS) and Aβ42, an aggregate-prone protein that causes Alzheimer's disease (AD), was identified. Structurally, Aβ42 presents a specific groove that is recognized by the amphiphilicity of LPS bait in a non-equilibrium manner. Functionally, the transient complex elicits a cellular response to clear extracellular Aβ42 deposits in neuronal cells. Since the impaired clearance of toxic Aβ42 deposits correlates with AD pathology, the non-equilibrium LPS and Aβ42 could represent a useful target for developing AD therapeutics.

A theoretical study of polymorphism in VQIVYK fibrils

The VQIVYK fragment from the Tau protein, also known as PHF6, is essential for aggregation of Tau into neurofibrillary lesions associated with neurodegenerative diseases. VQIVYK itself forms amyloid fibrils composed of paired β-sheets. Therefore, the full Tau protein and VQIVYK fibrils have been intensively investigated. A central issue in these studies is polymorphism, the ability of a protein to fold into more than one structure. Using all-atom molecular simulations, we generate five stable polymorphs of VQIVYK fibrils, establish their relative free energy with umbrella sampling methods, and identify the side chain interactions that provide stability. The two most stable polymorphs, which have nearly equal free energy, are formed by interdigitation of the mostly hydrophobic VIY "face" sides of the β-sheets. Another stable polymorph is formed by interdigitation of the QVK "back" sides. When we turn to examine structures from cryo-electron microscopy experiments on Tau filaments taken from diseased patients or generated in vitro, we find that the pattern of side chain interactions found in the two most stable face-to-face as well as the back-to-back polymorphs are recapitulated in amyloid structures of the full protein. Thus, our studies suggest that the interactions stabilizing PHF6 fibrils explain the amyloidogenicity of the VQIVYK motif within the full Tau protein and provide justification for the use of VQIVYK fibrils as a test bed for the design of molecules that identify or inhibit amyloid structures.

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

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

Introducing Virtual Oligomerization Inhibition to Identify Potent Inhibitors of Aβ Oligomerization

Amyloid-β (Aβ) oligomers are known as the most toxic form of Aβ peptides, and they are a major contributor to Alzheimer's disease. Therefore, developing antagonist screening methods for the formation of Aβ oligomers is urgent and of great interest. In this study, we introduce virtual oligomerization inhibition (VOI), a novel virtual screening protocol that applies atomistic simulation to quantitatively investigate the ability of a ligand in interfering Aβ oligomerization and the formation of Aβ oligomers. Results from the VOI performance on six known inhibitors of Aβ aggregation (brazilin, curcumin, EGCG, ELND005, resveratrol, and tacrine) are in excellent agreement with the results of expensive experiments. Moreover, VOI can reveal the mechanism and kinetics of the inhibition process at the atomistic level. VOI not only improves the efficiency of the antagonist screening for Aβ oligomerization but also reduces the cost of performing the task. Attractively, the principle of VOI can also be applied to inhibitor screening for the aggregation of other amyloid proteins/peptides.

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

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

Structural Analysis of a Trimer of β2-Microgloblin Fragment by Molecular Dynamics Simulations

A peptide β₂-m_21-31, which is a fragment from residue 21 to residue 31 of β₂-microgloblin, is experimentally known to self-assemble and form amyloid fibrils. In order to understand the mechanism of amyloid fibril formations, we applied the replica-exchange molecular dynamics method to the system consisting of three fragments of β₂-m_21-31. From the analyses on the temperature dependence, we found that there is a clear phase transition temperature in which the peptides aggregate with each other. Moreover, we found by the free energy analyses that there are two major stable states: One of them is like amyloid fibrils and the other is amorphous aggregates.

Biomolecular Assemblies: Moving from Observation to Predictive Design

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

Growth probability and formation time of the individual Oosawa-Kasai protein fibril

Protein fibrils are currently of great academic and practical interest because of their involvement in scores of severe human diseases and their promising use in various high-technology devices. The Oosawa-Kasai (OK) model of protein self-assembly into fibrils has been widely used to gain mechanistic insight into the process of fibril formation and growth. Here this model is employed to obtain exact and mathematically simple expressions for the probability P_{n} of an individual fibril of n protein monomers to grow to a macroscopically large size and for the mean time τ_{n} that such a fibril needs for its formation. These expressions quantify the increase of P_{n} and the decrease of τ_{n} with increasing the concentration of monomeric protein in the solution. When used for analysis of experimental P_{n} and τ_{n} data, they make it possible to determine the parameters characterizing fibril nucleation and growth in the framework of the OK model. Finally, an expression is found for the mean time of the first appearance of an n-sized fibril in the protein solution. The results obtained are applicable to the formation of other aggregates corresponding to the OK fibrils, such as the one-dimensional Kossel-Stranski crystals and Ising ferromagnets.

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.

Sequence dependent aggregation of peptides and fibril formation

Deciphering the links between amino acid sequence and amyloid fibril formation is key for understanding protein misfolding diseases. Here we use Monte Carlo simulations to study the aggregation of short peptides in a coarse-grained model with hydrophobic-polar (HP) amino acid sequences and correlated side chain orientations for hydrophobic contacts. A significant heterogeneity is observed in the aggregate structures and in the thermodynamics of aggregation for systems of different HP sequences and different numbers of peptides. Fibril-like ordered aggregates are found for several sequences that contain the common HPH pattern, while other sequences may form helix bundles or disordered aggregates. A wide variation of the aggregation transition temperatures among sequences, even among those of the same hydrophobic fraction, indicates that not all sequences undergo aggregation at a presumable physiological temperature. The transition is found to be the most cooperative for sequences forming fibril-like structures. For a fibril-prone sequence, it is shown that fibril formation follows the nucleation and growth mechanism. Interestingly, a binary mixture of peptides of an aggregation-prone and a non-aggregation-prone sequence shows the association and conversion of the latter to the fibrillar structure. Our study highlights the role of a sequence in selecting fibril-like aggregates and also the impact of a structural template on fibril formation by peptides of unrelated sequences.

Adaptive enhanced sampling with a path-variable for the simulation of protein folding and aggregation

In this article, we present a novel adaptive enhanced sampling molecular dynamics (MD) method for the accelerated simulation of protein folding and aggregation. We introduce a path-variable L based on the un-biased momenta p and displacements dq for the definition of the bias s applied to the system and derive 3 algorithms: general adaptive bias MD, adaptive path-sampling, and a hybrid method which combines the first 2 methodologies. Through the analysis of the correlations between the bias and the un-biased gradient in the system, we find that the hybrid methodology leads to an improved force correlation and acceleration in the sampling of the phase space. We apply our method on SPC/E water, where we find a conservation of the average water structure. We then use our method to sample dialanine and the folding of TrpCage, where we find a good agreement with simulation data reported in the literature. Finally, we apply our methodologies on the initial stages of aggregation of a hexamer of Alzheimer's amyloid β fragment 25-35 (Aβ 25-35) and find that transitions within the hexameric aggregate are dominated by entropic barriers, while we speculate that especially the conformation entropy plays a major role in the formation of the fibril as a rate limiting factor.

Reversible Assembly of a Drug Peptide into Amyloid Fibrils: A Dynamic Circular Dichroism Study

The common view on the amyloid fibril formation is that it is a multistep process that involves many oligomeric intermediate species, which leads to a high degree of polymorphism. This view derives from numerous kinetic studies whose vast majority was carried out with amyloid β fragments or other pathological amyloidogenic sequences. Yet, it is not clear whether the mechanisms inferred from these studies are universal and also apply to functional amyloids, in particular to peptide hormones which form reversible amyloid structures. In the present work, we study the self-assembly properties of atosiban, a nonapeptide drug, whose sequence is very close to those of the oxytocin and vasopressin hormones. We show that this very soluble peptide consistently self-assembles into 7 nm wide amyloid fibrils above a critical aggregation concentration (2-10 w/w % depending on the buffer conditions). The peptide system is characterized in details, from the monomeric to the assembled form, with osmotic concentration measurements, transmission electron microscopy, small-angle X-ray scattering, infrared and fluorescence spectroscopy, and circular dichroism (CD). We have followed in situ the fibril assembly with fluorescence and synchrotron radiation CD and noticed that the peptide undergoes conformational changes during the process. However, several lines of evidence point toward the association of monomers and dimers into fibrils without passing through oligomeric intermediate species contrary to what is usually reported for pathogenic amyloids. The native β-hairpin conformation of the monomer could explain the straightforward assembly. The tyrosine stacking is also shown to play an important role.

Molecular simulations of self-assembling bio-inspired supramolecular systems and their connection to experiments

In bionanotechnology, the field of creating functional materials consisting of bio-inspired molecules, the function and shape of a nanostructure only appear through the assembly of many small molecules together. The large number of building blocks required to define a nanostructure combined with the many degrees of freedom in packing small molecules has long precluded molecular simulations, but recent advances in computational hardware as well as software have made classical simulations available to this strongly expanding field. Here, we review the state of the art in simulations of self-assembling bio-inspired supramolecular systems. We will first discuss progress in force fields, simulation protocols and enhanced sampling techniques using recent examples. Secondly, we will focus on efforts to enable the comparison of experimentally accessible observables and computational results. Experimental quantities that can be measured by microscopy, spectroscopy and scattering can be linked to simulation output either directly or indirectly, via quantum mechanical or semi-empirical techniques. Overall, we aim to provide an overview of the various computational approaches to understand not only the molecular architecture of nanostructures, but also the mechanism of their formation.

An adaptive bias - hybrid MD/kMC algorithm for protein folding and aggregation

In this paper, we present a novel hybrid Molecular Dynamics/kinetic Monte Carlo (MD/kMC) algorithm and apply it to protein folding and aggregation in explicit solvent. The new algorithm uses a dynamical definition of biases throughout the MD component of the simulation, normalized in relation to the unbiased forces. The algorithm guarantees sampling of the underlying ensemble in dependency of one average linear coupling factor 〈α〉_τ. We test the validity of the kinetics in simulations of dialanine and compare dihedral transition kinetics with long-time MD-simulations. We find that for low 〈α〉_τ values, kinetics are in good quantitative agreement. In folding simulations of TrpCage and TrpZip4 in explicit solvent, we also find good quantitative agreement with experimental results and prior MD/kMC simulations. Finally, we apply our algorithm to study growth of the Alzheimer Amyloid Aβ 16-22 fibril by monomer addition. We observe two possible binding modes, one at the extremity of the fibril (elongation) and one on the surface of the fibril (lateral growth), on timescales ranging from ns to 8 μs.

Inhibition of GNNQQNY prion peptide aggregation by trehalose: a mechanistic view

Deposition of amyloid fibrils is the seminal event in the pathogenesis of numerous neurodegenerative diseases. The formation of this amyloid assembly is the manifestation of a cascade of structural transitions including toxic oligomer formation in the early stages of aggregation. Thus a viable therapeutic strategy involves the use of small molecular ligands to interfere with this assembly. In this perspective, we have explored the kinetics of aggregate formation of the fibril forming GNNQQNY peptide fragment from the yeast prion protein SUP35 using multiple all atom MD simulations with explicit solvent and provided mechanistic insights into the way trehalose, an experimentally known aggregation inhibitor, modulates the aggregation pathway. The results suggest that the assimilation process is impeded by different barriers at smaller and larger oligomeric sizes: the initial one being easily surpassed at higher temperatures and peptide concentrations. The kinetic profile demonstrates that trehalose delays the aggregation process by increasing both these activation barriers, specifically the latter one. It increases the sampling of small-sized aggregates that lack the beta sheet conformation. Analysis reveals that the barrier in the growth of larger stable oligomers causes the formation of multiple stable small oligomers which then fuse together bimolecularly. The PCA of 26 properties was carried out to deconvolute the events within the temporary lag phases, which suggested dynamism in lags involving an increase in interchain contacts and burial of SASA. The predominant growth route is monomer addition, which changes to condensation on account of a large number of depolymerisation events in the presence of trehalose. The favourable interaction of trehalose specifically with the sidechain of the peptide promotes crowding of trehalose molecules in its vicinity - the combination of both these factors imparts the observed behaviour. Furthermore, increasing trehalose concentration leads to faster expulsion of water molecules than interpeptide interactions. These expelled water molecules have larger translational movement, suggesting an entropy factor to favor the assembly process. Different conformations observed under this condition suggest the role of water molecules in guiding the morphology of the aggregates as well. A similar scenario exists on increasing peptide concentration.

Primary Fibril Nucleation of Aggregation Prone Tau Fragments PHF6 and PHF6

We performed replica exchange molecular dynamics and forward flux sampling simulations of hexapeptide VQIINK and VQIVYK systems, also known as, respectively, fragments PHF6* and PHF6 from the tau protein. Being a part of the microtubule binding region, these fragments are known to be aggregation prone, and at least one of them is a prerequisite for fibril formation of the tau protein. Using a coarse-grained force field, we establish the phase behavior of both fragments, and investigate the nucleation kinetics for the conversion into a β-sheet fibril. As the conversion is, in principle, a reversible process, we predict the rate constants for both the fibril formation and melting, and examine the corresponding mechanisms. Our simulations indicate that, while both fragments form disordered aggregates, only PHF6 is able to form β-sheet fibrils. This observation provides a possible explanation for the lack of available steric zipper crystal structures for PHF6*.

Protein Aggregation and Molecular Crowding: Perspectives From Multiscale Simulations

Cells are extremely crowded environments, thus the use of diluted salted aqueous solutions containing a single protein is too simplistic to mimic the real situation. Macromolecular crowding might affect protein structure, folding, shape, conformational stability, binding of small molecules, enzymatic activity, interactions with cognate biomolecules, and pathological aggregation. The latter phenomenon typically leads to the formation of amyloid fibrils that are linked to several lethal neurodegenerative diseases, but that can also play a functional role in certain organisms. The majority of molecular simulations performed before the last few years were conducted in diluted solutions and were restricted both in the timescales and in the system dimensions by the available computational resources. In recent years, several computational solutions were developed to get close to physiological conditions. In this review we summarize the main computational techniques used to tackle the issue of protein aggregation both in a diluted and in a crowded environment.

Advances in the Simulation of Protein Aggregation at the Atomistic Scale

Protein aggregation into highly structured amyloid fibrils is associated with various diseases including Alzheimer's disease, Parkinson's disease, and type II diabetes. Amyloids can also have normal biological functions and, in the future, could be used as the basis for novel nanoscale materials. However, a full understanding of the physicochemical forces that drive protein aggregation is still lacking. Such understanding is crucial for the development of drugs that can effectively inhibit aberrant amyloid aggregation and for the directed design of functional amyloids. Atomistic simulations can help understand protein aggregation. In particular, atomistic simulations can be used to study the initial formation of toxic oligomers which are hard to characterize experimentally and to understand the difference in aggregation behavior between different amyloidogenic peptides. Here, we review the latest atomistic simulations of protein aggregation, concentrating on amyloidogenic protein fragments, and provide an outlook for the future in this field.