Spontaneous fibril formation by polyalanines; discontinuous molecular dynamics simulations

Exploring the aggregation of amyloid-β 42 through Monte Carlo simulations

Coarse-grained Monte Carlo simulations are performed for a disordered protein, amyloid-β 42 to identify the interactions and understand the mechanism of its aggregation. A statistical potential is developed from a selected dataset of intrinsically disordered proteins, which accounts for the respective contributions of the bonded and non-bonded potentials. While, the bonded potential comprises the bond, bend, and dihedral constraints, the nonbonded interactions include van der Waals interactions, hydrogen bonds, and the two-body potential. The two-body potential captures the features of both hydrophobic and electrostatic interactions that brings the chains at a contact distance, while the repulsive van der Waals interactions prevent them from a collapse. Increased two-body hydrophobic interactions facilitate the formation of amorphous aggregates rather than the fibrillar ones. The formation of aggregates is validated from the interchain distances, and the total energy of the system. The aggregate is structurally characterized by the root-mean-square deviation, root-mean-square fluctuation and the radius of gyration. The aggregates are characterized by a decrease in SASA, an increase in the non-local interactions and a distinct free energy minimum relative to that of the monomeric state of amyloid-β 42. The hydrophobic residues help in nucleation, while the charged residues help in oligomerization and aggregation.

Advances in the understanding of protein misfolding and aggregation through molecular dynamics simulation

Aberrant protein folding known as protein misfolding is counted as one of the striking factors of neurodegenerative diseases. The extensive range of pathologies caused by protein misfolding, aggregation and subsequent accumulation are mainly classified into either gain of function diseases or loss of function diseases. In order to seek for novel strategies for treatment and diagnosis of neurodegenerative diseases, insights into the mechanism of misfolding and aggregation is essential. A comprehensive knowledge on the factors influencing misfolding and aggregation is required as well. An extensive experimental study on protein aggregation is somewhat challenging due to the insoluble and noncrystalline nature of amyloid fibrils. Thus there has been a growing use of computational approaches including Monte Carlo simulation, docking simulation, molecular dynamics simulation in the study of protein misfolding and aggregation. The review presents a discussion on molecular dynamics simulation alone as to how it has emerged as a promising tool in the understanding of protein misfolding and aggregation in general, detailing upon three different aspects considering four misfold prone proteins in particular. It is noticeable that all four proteins considered in this review i.e prion, superoxide dismutase1, huntingtin and amyloid β are linked to chronic neurodegenerative diseases with debilitating effects. Initially the review elaborates on the factors influencing the misfolding and aggregation. Next, it addresses our current understanding of the amyloid structures and the associated aggregation mechanisms, finally, summarizing the contribution of this computational tool in the search for therapeutic strategies against the respective protein-deposition diseases.

A hybrid coarse-grained model for structure, solvation and assembly of lipid-like peptides

Reconstituted photosynthetic proteins which are activated upon exposure to solar energy hold enormous potential for powering future solid state devices and solar cells. The functionality and integration of these proteins into such devices has been successfully enabled by lipid-like peptides. Yet, a fundamental understanding of the organization of these peptides with respect to the photosynthetic proteins and themselves remains unknown and is critical for guiding the design of such light-activated devices. This study investigates the relative organization of one such peptide sequence V₆K₂ (V: valine and K: lysine) within assemblies. Given the expansive spatiotemporal scales associated with this study, a hybrid coarse-grained (CG) model which captures the structure, conformation and aggregation of the peptide is adopted. The CG model uses a combination of iterative Boltzmann inversion and force matching to provide insight into the relative organization of V₆K₂ in assemblies. The CG model reproduces the structure of a V₆K₂ peptide sequence along with its all atom (AA) solvation structure. The relative organization of multiple peptides in an assembly, as captured by CG simulations, is in agreement with corresponding results from AA simulations. Also, a backmapping procedure reintroduces the AA details of the peptides within the aggregates captured by the CG model to demonstrate the relative organization of the peptides. Furthermore, a large number of peptides self-assemble into an elongated micelle in the CG simulation, which is consistent with experimental findings. The coarse-graining procedure is tested for transferability to longer peptide sequences, and hence can be extended to other amphiphilic peptide sequences.

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.

Protein aggregation: in silico algorithms and applications

Protein aggregation is a topic of immense interest to the scientific community due to its role in several neurodegenerative diseases/disorders and industrial importance. Several in silico techniques, tools, and algorithms have been developed to predict aggregation in proteins and understand the aggregation mechanisms. This review attempts to provide an essence of the vast developments in in silico approaches, resources available, and future perspectives. It reviews aggregation-related databases, mechanistic models (aggregation-prone region and aggregation propensity prediction), kinetic models (aggregation rate prediction), and molecular dynamics studies related to aggregation. With a multitude of prediction models related to aggregation already available to the scientific community, the field of protein aggregation is rapidly maturing to tackle new applications.

Inhibition potential evaluation of two synthetic bis-indole compounds on amyloid fibrillation: a molecular simulation study

Protein aggregation is known as the main mechanism of amyloid fibrillation in amyloidosis diseases. Recent studies confirmed that compounds with one or two indole rings have inhibitory potential against amyloid fibrillation. Herein, the interaction of two similar compounds 'bis(indolyl)-2-methyl-phenyl-methene' and 'bis(indolyl)-2-chloro-phenyl-methene' with an amyloid core model was investigated. To this aim, molecular docking and all-atom molecular dynamics (MD) simulations were used. Docking results between aggregation-prone region (APR) of hen egg-white lysozyme (HEWL) and either of ligands showed that they interact with different residues of the APR (amyloid fibril nucleus). According to MD results, bis(indolyl)-2-methyl-phenyl-methene made a distance between the two cores, which was 1.5 times greater than that bis(indolyl)-2-chloro-phenyl-methene made. Analysis of RMSD/RMSF values revealed that bis(indolyl)-2-methyl-phenyl-methene stabilized strands of A and B, while destabilized strands C and D. The hydrophobic 'methyl' functional group in bis(indolyl)-2-methyl-phenyl-methene facilitate its deep penetration between core nuclei, via destabilizing outer strands of C and D. Considering this fact that results of this study are in agreement with experimental findings, details of the discovered mechanism of interaction between ligands and HEWL's APR would be inspiring for further anti-fibrillation drug designs.Communicated by Ramaswamy H. Sarma.

The balance between side-chain and backbone-driven association in folding of the α-helical influenza A transmembrane peptide

The correct balance between attractive, repulsive and peptide hydrogen bonding interactions must be attained for proteins to fold correctly. To investigate these important contributors, we sought a comparison of the folding between two 25-residues peptides, the influenza A M2 protein transmembrane domain (M2TM) and the 25-Ala (Ala₂₅ ). M2TM forms a stable α-helix as is shown by circular dichroism (CD) experiments. Molecular dynamics (MD) simulations with adaptive tempering show that M2TM monomer is more dynamic in nature and quickly interconverts between an ensemble of various α-helical structures, and less frequently turns and coils, compared to one α-helix for Ala₂₅ . DFT calculations suggest that folding from the extended structure to the α-helical structure is favored for M2TM compared with Ala₂₅ . This is due to CH⋯O attractive interactions which favor folding to the M2TM α-helix, and cannot be described accurately with a force field. Using natural bond orbital (NBO) analysis and quantum theory atoms in molecules (QTAIM) calculations, 26 CH⋯O interactions and 22 NH⋯O hydrogen bonds are calculated for M2TM. The calculations show that CH⋯O hydrogen bonds, although individually weaker, have a cumulative effect that cannot be ignored and may contribute as much as half of the total hydrogen bonding energy, when compared to NH⋯O, to the stabilization of the α-helix in M2TM. Further, a strengthening of NH⋯O hydrogen bonding interactions is calculated for M2TM compared to Ala₂₅ . Additionally, these weak CH⋯O interactions can dissociate and associate easily leading to the ensemble of folded structures for M2TM observed in folding MD simulations.

Theoretical and computational advances in protein misfolding

Misfolded proteins escape the cellular quality control mechanism and fail to fold properly or remain correctly folded leading to a loss in their functional specificity. Thus misfolding of proteins cause a large number of very different diseases ranging from errors in metabolism to various types of complex neurodegenerative diseases. A theoretical and computational perspective of protein misfolding is presented with a special emphasis on its salient features, mechanism and consequences. These insights quantitatively analyze different determinants of misfolding, that may be applied to design disease specific molecular targets.

A hybrid, bottom-up, structurally accurate, Go¯-like coarse-grained protein model

Coarse-grained (CG) protein models in the structural biology literature have improved over the years from being simple tools to understand general folding and aggregation driving forces to capturing detailed structures achieved by actual folding sequences. Here, we ask whether such models can be developed systematically from recent advances in bottom-up coarse-graining methods without relying on bioinformatic data (e.g., protein data bank statistics). We use relative entropy coarse-graining to develop a hybrid CG but Go¯-like CG peptide model, hypothesizing that the landscape of proteinlike folds is encoded by the backbone interactions, while the sidechain interactions define which of these structures globally minimizes the free energy in a unique native fold. To construct a model capable of capturing varied secondary structures, we use a new extended ensemble relative entropy method to coarse-grain based on multiple reference atomistic simulations of short polypeptides with varied α and β character. Subsequently, we assess the CG model as a putative protein backbone forcefield by combining it with sidechain interactions based on native contacts but not incorporating native distances explicitly, unlike standard Go¯ models. We test the model's ability to fold a range of proteins and find that it achieves high accuracy (∼2 Å root mean square deviation resolution for both short sequences and large globular proteins), suggesting the strong role that backbone conformational preferences play in defining the fold landscape. This model can be systematically extended to non-natural amino acids and nonprotein polymers and sets the stage for extensions to non-Go¯ models with sequence-specific sidechain interactions.

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.

Conformational preferences and phase behavior of intrinsically disordered low complexity sequences: insights from multiscale simulations

While many proteins and protein regions utilize a complex repertoire of amino acids to achieve their biological function, a subset of protein sequences are enriched in a reduced set of amino acids. These so-called low complexity (LC) sequences, specifically intrinsically disordered variants of LC sequences, have been the focus of recent investigations owing to their roles in a range of biological functions, specifically phase separation. Computational studies of LC sequences have provided rich insights into their behavior both as individual proteins in dilute solutions and as the drivers and modulators of higher-order assemblies. Here, we review how simulations performed across distinct resolutions have provided different types of insights into the biological role of LC sequences.

Simulations and Experiments Delineate Amyloid Fibrilization by Peptides Derived from Glaucoma-Associated Myocilin

Mutant myocilin aggregation is associated with inherited open angle glaucoma, a prevalent optic neuropathy leading to blindness. Comprehension of mutant myocilin aggregation is of fundamental importance to glaucoma pathogenesis and ties glaucoma to amyloid diseases such as Alzheimer's. Here, we probe the aggregation properties of peptides derived from the myocilin olfactomedin domain. Peptides P1 (residues 326-337) and P3 (residues 426-442) were identified previously to form amyloids. Coarse-grained discontinuous molecular dynamics simulations using the PRIME20 force field (DMD/PRIME20) predict that P1 and P3 are aggregation-prone; P1 consistently forms fibrillar aggregates with parallel in-register β-sheets, whereas P3 forms β-sheet-containing aggregates without distinct order. Natural abundance ¹³C solid-state NMR spectra validate that aggregated P1 exhibits amyloid signatures and is more homogeneous than aggregated P3. DMD/PRIME20 simulations provide a viable method to predict peptide aggregation propensities and aggregate structure/order which cannot be accessed by bioinformatics or readily attained experimentally.

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.

HyRes: a coarse-grained model for multi-scale enhanced sampling of disordered protein conformations

Efficient coarse-grained (CG) models can be coupled with atomistic force fields to accelerate the sampling of atomistic energy landscapes in the multi-scale enhanced sampling (MSES) framework. This approach may be particularly suitable for generating atomistic conformational ensembles of intrinsically disordered proteins (IDPs). While MSES is relatively robust to inherent CG artifacts, achieving optimal sampling efficiency requires CG modeling to generate the local and long-range fluctuations that are largely consistent with those at the atomistic level. Here, we describe a new hybrid resolution CG model (HyRes) for MSES simulations of disordered protein states, which is specifically designed to provide semi-quantitative secondary structure propensities together with a qualitative description of long-range nonspecific interactions. The HyRes model contains an atomistic description of the backbone with intermediate resolution side chains. The secondary structure propensities are tuned by adjusting the backbone hydrogen-bonding strength and the ϕ/ψ torsion profile. The sizes and covalent geometries of the side chains are parameterized to reproduce distributions derived from atomistic simulations. Lennard-Jones parameters for sidechain beads are assigned to reproduce statistical potentials derived from the protein structural database, and then globally parameterized with nonspecific electrostatic interactions to reproduce the free energy profiles of pair wise interactions and the key conformational properties of model peptides. Application of HyRes to MSES simulations of small IDPs suggests that it is capable of driving faster structural transitions at the atomistic level and increasing the convergence rate compared to the Cα-only Gō-like models previously utilized. With further optimization, we believe that the new CG model could greatly improve the efficiency of MSES simulations of the larger and more complex IDPs frequently involved in cellular signalling and regulation.

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.

A Protocol for the Design of Protein and Peptide Nanostructure Self-Assemblies Exploiting Synthetic Amino Acids

In recent years there has been increasing interest in nanostructure design based on the self-assembly properties of proteins and polymers. Nanodesign requires the ability to predictably manipulate the properties of the self-assembly of autonomous building blocks, which can fold or aggregate into preferred conformational states. The design includes functional synthetic materials and biological macromolecules. Autonomous biological building blocks with available 3D structures provide an extremely rich and useful resource. Structural databases contain large libraries of protein molecules and their building blocks with a range of sizes, shapes, surfaces, and chemical properties. The introduction of engineered synthetic residues or short peptides into these building blocks can greatly expand the available chemical space and enhance the desired properties. Herein, we summarize a protocol for designing nanostructures consisting of self-assembling building blocks, based on our recent works. We focus on the principles of nanostructure design with naturally occurring proteins and synthetic amino acids, as well as hybrid materials made of amyloids and synthetic polymers.

Aggregation of Chameleon Peptides: Implications of α-Helicity in Fibril Formation

We investigate the relationship between the inherent secondary structure and aggregation propensity of peptides containing chameleon sequences (i.e., sequences that can adopt either α or β structure depending on context) using a combination of replica exchange molecular dynamics simulations, ion-mobility mass spectrometry, circular dichroism, and transmission electron microscopy. We focus on an eight-residue long chameleon sequence that can adopt an α-helical structure in the context of the iron-binding protein from Bacillus anthracis (PDB id 1JIG ) and a β-strand in the context of the baculovirus P35 protein (PDB id 1P35 ). We show that the isolated chameleon sequence is intrinsically disordered, interconverting between α-helical and β-rich conformations. The inherent conformational plasticity of the sequence can be constrained by addition of flanking residues with a given secondary structure propensity. Intriguingly, we show that the chameleon sequence with helical flanking residues aggregates rapidly into fibrils, whereas the chameleon sequence with flanking residues that favor β-conformations has weak aggregation propensity. This work sheds new insights into the possible role of α-helical intermediates in fibril formation.

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.

Competition between surface adsorption and folding of fibril-forming polypeptides

Self-assembly of polypeptides into fibrillar structures can be initiated by planar surfaces that interact favorably with certain residues. Using a coarse-grained model, we systematically studied the folding and adsorption behavior of a β-roll forming polypeptide. We find that there are two different folding pathways depending on the temperature: (i) at low temperature, the polypeptide folds in solution into a β-roll before adsorbing onto the attractive surface; (ii) at higher temperature, the polypeptide first adsorbs in a disordered state and folds while on the surface. The folding temperature increases with increasing attraction as the folded β-roll is stabilized by the surface. Surprisingly, further increasing the attraction lowers the folding temperature again, as strong attraction also stabilizes the adsorbed disordered state, which competes with folding of the polypeptide. Our results suggest that to enhance the folding, one should use a weakly attractive surface. They also explain the recent experimental observation of the nonmonotonic effect of charge on the fibril formation on an oppositely charged surface [C. Charbonneau et al., ACS Nano 8, 2328 (2014)].

Solvent effects on kinetic mechanisms of self-assembly by peptide amphiphiles via molecular dynamics simulations

Peptide amphiphiles are known to form a variety of distinctive self-assembled nanostructures (including cylindrical nanofibers in hydrogels) dependent upon the solvent conditions. Using a novel coarse-grained model, large-scale molecular dynamics simulations are performed on a system of 800 peptide amphiphiles (sequence, palmitoyl-Val3Ala3Glu3) to elucidate kinetic mechanisms of molecular assembly as a function of the solvent conditions. The assembly process is found to occur via a multistep process with transient intermediates that ultimately leads to the stabilized nanostructures including open networks of β-sheets, cylindrical nanofibers, and elongated micelles. Different kinetic mechanisms are compared in terms of peptide secondary structures, solvent-accessible surface area, radius of gyration, relative shape anisotropy, intra/intermolecular interactions, and aggregate size dynamics to provide insightful information for the design of functional biomaterials.

Effects of hydrophobic interaction strength on the self-assembled structures of model peptides

Stable and ordered self-assembled peptide nanostructures are formed as a result of cooperative effects of various relatively weak intermolecular interactions. We systematically studied the influence of hydrophobic interaction strength and temperature on the self-assembly of peptides with a coarse-grained model by Monte Carlo simulations. The simulation results show a rich phase behavior of peptide self-assembly, indicating that the formation and morphology of peptide assemblies may be tuned by varying the temperature and the strength of hydrophobic interactions. There exist optimal combinations of temperature and hydrophobic interaction strength where ordered fibrillar nanostructures are readily formed. Our simulation results not only facilitate the understanding of the self-assembly behavior of peptides at the molecular level, but also provide useful insights into the development of fabrication strategies for high-quality peptide fibrils.

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.

Length-dependent β-sheet growth mechanisms of polyalanine peptides in water and on hydrophobic surfaces

Fibrillar assemblies by peptides are becoming one of the most promising nanomaterials due to their exceptional properties. The self-assembly of peptides into β sheets is a critical step in the fibrillization pathway. We investigated the length-dependent β-sheet growth mechanisms of polyalanine [poly(A)] peptides consisting of 6 to 24 alanines (A6 to A24) in water and on the hydrophobic surface, respectively, by molecular dynamics simulations. β-sheet growth behavior in water fits negative exponential growth model, showing that β-sheet growth rate decays exponentially with time. Meanwhile, increasing chain length leads to an accelerated decay of the β-sheet growth rate. By contrast, β-sheet growth on the surface from A6 to A18 occurs in two consecutive stages, both of which fit linear growth models. β-sheet growth rate in the first stage increases as chain length is increased, while the intermediate length peptide A12 has the highest β-sheet growth rate in the second stage. β-sheet growth behavior of A24 on the surface still fits negative exponential model. Overall, the hydrophobic surface accelerates β-sheet growth by enhancing local concentration and reducing conformational entropy of poly(A) peptide, and the β-sheet growth of the intermediate length peptide A12 is the fastest on the surface. Our simulation results shed light on understanding the accelerated peptide fibrillization on the hydrophobic surface.

Kinetic theory of amyloid fibril templating

The growth of amyloid fibrils requires a disordered or partially unfolded protein to bind to the fibril and adapt the same conformation and alignment established by the fibril template. Since the H-bonds stabilizing the fibril are interchangeable, it is inevitable that H-bonds form between incorrect pairs of amino acids which are either incorporated into the fibril as defects or must be broken before the correct alignment can be found. This process is modeled by mapping the formation and breakage of H-bonds to a one-dimensional random walk. The resulting microscopic model of fibril growth is governed by two timescales: the diffusion time of the monomeric proteins, and the time required for incorrectly bound proteins to unbind from the fibril. The theory predicts that the Arrhenius behavior observed in experiments is due to off-pathway states rather than an on-pathway transition state. The predicted growth rates are in qualitative agreement with experiments on insulin fibril growth rates as a function of protein concentration, denaturant concentration, and temperature. These results suggest a templating mechanism where steric clashes due to a single mis-aligned molecule prevent the binding of additional molecules.

Interplay between folding and assembly of fibril-forming polypeptides

Polypeptides can self-assemble into hierarchically organized fibrils consisting of a stack of individually folded polypeptides driven together by hydrophobic interaction. Using a coarse-grained model, we systematically studied this self-assembly as a function of temperature and hydrophobicity of the residues on the outside of the building block. We find the self-assembly can occur via two different pathways-a random aggregation-folding route and a templated-folding process-thus indicating a strong coupling between folding and assembly. The simulation results can explain experimental evidence that assembly through stacking of folded building blocks is rarely observed, at the experimental concentrations. The model thus provides a generic picture of hierarchical fibril formation.

Nucleation process of a fibril precursor in the C-terminal segment of amyloid-β

By extended atomistic simulations in explicit solvent and bias-exchange metadynamics, we study the aggregation process of 18 chains of the C-terminal segment of amyloid-β, an intrinsically disordered protein involved in Alzheimer's disease and prone to form fibrils. Starting from a disordered aggregate, we are able to observe the formation of an ordered nucleus rich in beta sheets. The rate limiting step in the nucleation pathway involves crossing a barrier of approximately 40 kcal/mol and is associated with the formation of a very specific interdigitation of the side chains belonging to different sheets. This structural pattern is different from the one observed experimentally in a microcrystal of the same system, indicating that the structure of a "nascent" fibril may differ from the one of an "extended" fibril.

Reduced atomic pair-interaction design (RAPID) model for simulations of proteins

Increasingly, theoretical studies of proteins focus on large systems. This trend demands the development of computational models that are fast, to overcome the growing complexity, and accurate, to capture the physically relevant features. To address this demand, we introduce a protein model that uses all-atom architecture to ensure the highest level of chemical detail while employing effective pair potentials to represent the effect of solvent to achieve the maximum speed. The effective potentials are derived for amino acid residues based on the condition that the solvent-free model matches the relevant pair-distribution functions observed in explicit solvent simulations. As a test, the model is applied to alanine polypeptides. For the chain with 10 amino acid residues, the model is found to reproduce properly the native state and its population. Small discrepancies are observed for other folding properties and can be attributed to the approximations inherent in the model. The transferability of the generated effective potentials is investigated in simulations of a longer peptide with 25 residues. A minimal set of potentials is identified that leads to qualitatively correct results in comparison with the explicit solvent simulations. Further tests, conducted for multiple peptide chains, show that the transferable model correctly reproduces the experimentally observed tendency of polyalanines to aggregate into β-sheets more strongly with the growing length of the peptide chain. Taken together, the reported results suggest that the proposed model could be used to succesfully simulate folding and aggregation of small peptides in atomic detail. Further tests are needed to assess the strengths and limitations of the model more thoroughly.

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.

DPD Simulation of Protein Conformations: From α-Helices to β-Structures

We suggest a coarse-grained model for DPD simulations of polypeptides in solutions. The model mimics hydrogen bonding that stabilizes α-helical and β-structures using dissociable Morse bonds between quasiparticles representing the peptide groups amenable to hydrogen bonding. We demonstrate the capabilities of the model by simulating transitions between coil-like, globular, α-helical, and β-hairpin configurations of model peptides, varying Morse potential parameters, the hydrophobicities of residue side chains, and pH, which determines the charges of residue side chains. We construct a model triblock polypeptide mimicking the sequence of residues α-synuclein at two different pHs. The conformations of this model polypeptide depend on pH similarly to the behavior observed experimentally. The suggested approach to accounting for hydrogen bond formation within the general DPD framework may make the DPD method a competitive alternative to CGMD for modeling equilibrium and dynamic properties of proteins and polypeptides, especially during their transport in confined environments.

Nanomaterials design and tests for neural tissue engineering

Nanostructured scaffolds recently showed great promise in tissue engineering: nanomaterials can be tailored at the molecular level and scaffold morphology may more closely resemble features of extracellular matrix components in terms of porosity, framing and biofunctionalities. As a consequence, both biomechanical properties of scaffold microenvironments and biomaterial-protein interactions can be tuned, allowing for improved transplanted cell engraftment and better controlled diffusion of drugs. Easier said than done, a nanotech-based regenerative approach encompasses different fields of know-how, ranging from in silico simulations, nanomaterial synthesis and characterization at the nano-, micro- and mesoscales to random library screening methods (e.g. phage display), in vitro cellular-based experiments and validation in animal models of the target injury. All of these steps of the "assembly line" of nanostructured scaffolds are tightly interconnected both in their standard analysis techniques and in their most recent breakthroughs: indeed their efforts have to jointly provide the deepest possible analyses of the diverse facets of the challenging field of neural tissue engineering. The purpose of this review is therefore to provide a critical overview of the recent advances in and drawbacks and potential of each mentioned field, contributing to the realization of effective nanotech-based therapies for the regeneration of peripheral nerve transections, spinal cord injuries and brain traumatic injuries. Far from being the ultimate overview of such a number of topics, the reader will acknowledge the intrinsic complexity of the goal of nanotech tissue engineering for a conscious approach to the development of a regenerative therapy and, by deciphering the thread connecting all steps of the research, will gain the necessary view of its tremendous potential if each piece of stone is correctly placed to work synergically in this impressive mosaic.

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.

Structural transitions and oligomerization along polyalanine fibril formation pathways from computer simulations

The results of a computer simulation study of the aggregation kinetics of a large system of model peptides with particular focus on the formation of intermediates are presented. Discontinuous molecular dynamic simulations were used in combination with our intermediate-resolution protein model, PRIME, to simulate the aggregation of a system of 192 polyalanine (KA(14) K) peptides at a concentration of 5 mM and a reduced temperature of T* = 0.13 starting from a random configuration and ending in the assembly of a fibrillar structure. The population of various structures, including free monomers, beta sheets, amorphous aggregates, hybrid aggregates, and fibrils, and the transitions between the structures were tracked over the course of 30 independent simulations and averaged together. The aggregation pathway for this system starts with the association of free monomers into small amorphous aggregates that then grow to moderate size by incorporating other free monomers or merging with other small amorphous aggregates. These then rearrange into either small beta sheets or hybrid aggregates formed by association between unstructured chains and beta sheets, both of which grow in size by adding free monomer chains or other small aggregates, one at a time. Fibrillar structures are formed initially either by the stacking of beta sheets, rearrangement of hybrid aggregates or association between beta sheets and hybrid aggregates. They grow by the addition of beta sheets, hybrid aggregates, and other small fibrillar structures. The rearrangement of amorphous aggregates into beta sheets is a critical and necessary step in the fibril formation pathway.

Coarse-grained simulations of protein aggregation

Protein aggregation is believed to be responsible for a number of human diseases and limits the yields of pharmaceutical proteins during production. Computer simulations can be used to develop novel experimentally testable hypotheses pertaining to aggregation. While all-atom simulations with explicit solvent are too computationally intensive to address the multitude of relevant time scales, coarse-grained models make it possible to observe the transition of monomers to an equilibrium containing aggregates. Here, we provide the reader with background information and a list of steps for setting up, performing, and analyzing computer simulations of aggregating coarse-grained (CG) proteins.

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.

Inversion of the balance between hydrophobic and hydrogen bonding interactions in protein folding and aggregation

Identifying the forces that drive proteins to misfold and aggregate, rather than to fold into their functional states, is fundamental to our understanding of living systems and to our ability to combat protein deposition disorders such as Alzheimer's disease and the spongiform encephalopathies. We report here the finding that the balance between hydrophobic and hydrogen bonding interactions is different for proteins in the processes of folding to their native states and misfolding to the alternative amyloid structures. We find that the minima of the protein free energy landscape for folding and misfolding tend to be respectively dominated by hydrophobic and by hydrogen bonding interactions. These results characterise the nature of the interactions that determine the competition between folding and misfolding of proteins by revealing that the stability of native proteins is primarily determined by hydrophobic interactions between side-chains, while the stability of amyloid fibrils depends more on backbone intermolecular hydrogen bonding interactions.

In order to carry out their biological functions, most proteins fold into well-defined conformations known as native states. Failure to fold, or to remain folded correctly, may result in misfolding and aggregation, which are processes associated with a wide range of highly debilitating, and so far incurable, human conditions that include Alzheimer's and Parkinson's diseases and type II diabetes. In our work we investigate the nature of the fundamental interactions that are responsible for the folding and misfolding behaviour of proteins, finding that interactions between protein side-chains play a major role in stabilising native states, whilst backbone hydrogen bonding interactions are key in determining the stability of amyloid fibrils.

Length-dependent aggregation of uninterrupted polyalanine peptides

Polyalanine (polyA) is the third-most prevalent homopeptide repeat in eukaryotes, behind polyglutamine and polyasparagine. Abnormal expansion of the polyA repeat is linked to at least nine human diseases, and the disease mechanism likely involves enhanced length-dependent aggregation. Because of the simplicity of its side chain, polyA has been a favorite target of computational studies, and because of their tendency to fold into α-helix, peptides containing polyA-rich domains have been a popular experimental subject. However, experimental studies on uninterrupted polyA are very limited. We synthesized polyA peptides containing uninterrupted sequences of 7 to 25 alanines (A7 to A25) and characterized their length-dependent conformation and aggregation properties. The peptides were primarily disordered, with a modest component of α-helix that increased with increasing length. From measurements of mean distance spanned by the polyA segment, we concluded that physiological buffers are neutral solvents for shorter polyA peptides and poor solvents for longer peptides. At moderate concentration and near-physiological temperature, polyA assembled into soluble oligomers, with a sharp transition in oligomer physical properties between A19 and A25. With A19, oligomers were large, contained only a small fraction of the total peptide mass, and slowly grew into loose clusters, while A25 rapidly and completely assembled into small stable oligomers of ~7 nm radius. At high temperatures, A19 assembled into fibrils, but A25 precipitated as dense, micrometer-sized particles. A comparison of these results to those obtained with polyglutamine peptides of similar design sheds light on the role of the side chain in regulating conformation and aggregation.

Lattice model of oligonucleotide hybridization in solution. I. Model and thermodynamics

A coarse-grained lattice model of DNA oligonucleotides is proposed to investigate the general mechanisms by which single-stranded oligonucleotides hybridize to their complementary strands in solution. The model, based on a high-coordination cubic lattice, is simple enough to allow the direct simulation of DNA solutions, yet capturing how the fundamental thermodynamic processes are microscopically encoded in the nucleobase sequences. Physically relevant interactions are considered explicitly, such as interchain excluded volume, anisotropic base-pairing and base-stacking, and single-stranded bending rigidity. The model is studied in detail by a specially adapted Monte Carlo simulation method, based on parallel tempering and biased trials, which is designed to overcome the entropic and enthalpic barriers associated with the sampling of hybridization events of multiple single-stranded chains in solution. This methodology addresses both the configurational complexity of bringing together two complementary strands in a favorable orientation (entropic barrier) and the energetic penalty of breaking apart multiple associated bases in a double-stranded state (enthalpic barrier). For strands with sequences restricted to nonstaggering association and homogeneous pairing and stacking energies, base-pairing is found to dominate the hybridization over the translational and conformational entropy. For strands with sequence-dependent pairing corresponding to that of DNA, the complex dependence of the model's thermal stability on concentration, sequence, and degree of complementarity is shown to be qualitatively and quantitatively consistent both with experiment and with the predictions of statistical mechanical models.

Steric zipper formed by hydrophobic peptide fragment of Syrian hamster prion protein

Steric zippers, where the residues of two neighboring β-sheet layers are tightly interdigitated, have been proposed as fundamental structural units of amyloid fibrils by Eisenberg and co-workers. The steric zipper formed by polypeptides containing the palindromic sequence AGAAAAGA has a distinctive feature that the distance between two interdigitated β-sheet layers is comparable to the interstrand distance of the individual β-sheet. This structural motif is of great interest in the study of prion disease because the AGAAAAGA sequence is highly conserved in prion proteins of different species. In this work, the amyloid fibrils formed by the polypeptides of PrP(113-127), viz. Ac-AGAAAAGAVVGGLGG-NH(2), are taken as the model compound to investigate the biophysical principles governing the steric zipper formation. The target fibrils adopt the structural motif of class 7 steric zipper, which is formed by stacking of antiparallel β-sheet layers with residue 117 + k forming backbone hydrogen bonds to residue 120 - k. Implication of our results in the infectivity of scrapie prion is briefly discussed.

Atomistic theory of amyloid fibril nucleation

We consider the nucleation of amyloid fibrils at the molecular level when the process takes place by a direct polymerization of peptides or protein segments into β-sheets. Employing the atomistic nucleation theory (ANT), we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) composed of successively layered β-sheets. The application of this expression to a recently studied peptide system allows us to determine the size of the fibril nucleus, the fibril nucleation work, and the fibril nucleation rate as functions of the supersaturation of the protein solution. Our analysis illustrates the unique feature of ANT that the size of the fibril nucleus is a constant integer in a given supersaturation range. We obtain the ANT nucleation rate and compare it with the rates determined previously in the scope of the classical nucleation theory (CNT) and the corrected classical nucleation theory (CCNT). We find that while the CNT nucleation rate is orders of magnitude greater than the ANT one, the CCNT and ANT nucleation rates are in very good quantitative agreement. The results obtained are applicable to homogeneous nucleation, which occurs when the protein solution is sufficiently pure and/or strongly supersaturated.

Extending the PRIME model for protein aggregation to all 20 amino acids

We extend PRIME, an intermediate-resolution protein model previously used in simulations of the aggregation of polyalanine and polyglutamine, to the description of the geometry and energetics of peptides containing all 20 amino acid residues. The 20 amino acid side chains are classified into 14 groups according to their hydrophobicity, polarity, size, charge, and potential for side chain hydrogen bonding. The parameters for extended PRIME, called PRIME 20, include hydrogen-bonding energies, side chain interaction range and energy, and excluded volume. The parameters are obtained by applying a perceptron-learning algorithm and a modified stochastic learning algorithm that optimizes the energy gap between 711 known native states from the PDB and decoy structures generated by gapless threading. The number of independent pair interaction parameters is chosen to be small enough to be physically meaningful yet large enough to give reasonably accurate results in discriminating decoys from native structures. The most physically meaningful results are obtained with 19 energy parameters.