Molecular dynamics simulations of spontaneous fibril formation by random-coil peptides

Amyloidogenesis abolished by proline substitutions but enhanced by lipid binding

The influence of lipid molecules on the aggregation of a highly amyloidogenic segment of human islet amyloid polypeptide, hIAPP20-29, and the corresponding sequence from rat has been studied by all-atom replica exchange molecular dynamics (REMD) simulations with explicit solvent model. hIAPP20-29 fragments aggregate into partially ordered beta-sheet oligomers and then undergo large conformational reorganization and convert into parallel/antiparallel beta-sheet oligomers in mixed in-register and out-of-register patterns. The hydrophobic interaction between lipid tails and residues at positions 23-25 is found to stabilize the ordered beta-sheet structure, indicating a catalysis role of lipid molecules in hIAPP20-29 self-assembly. The rat IAPP variants with three proline residues maintain unstructured micelle-like oligomers, which is consistent with non-amyloidogenic behavior observed in experimental studies. Our study provides the atomic resolution descriptions of the catalytic function of lipid molecules on the aggregation of IAPP peptides.

Simulations of nucleation and elongation of amyloid fibrils

We present a coarse-grained model for the growth kinetics of amyloid fibrils from solutions of peptides and address the fundamental mechanism of nucleation and elongation by using a lattice Monte Carlo procedure. We reproduce the three main characteristics of nucleation of amyloid fibrils: (1) existence of lag time, (2) occurrence of a critical concentration, and (3) seeding. We find the nucleation of amyloid fibrils to require a quasi-two-dimensional configuration, where a second layer of beta sheet must be formed adjunct to a first layer, which in turn leads to a highly cooperative nucleation barrier. The elongation stage is found to involve the Ostwald ripening (evaporation-condensation) mechanism, whereby bigger fibrils grow at the expense of smaller ones. This new mechanism reconciles the debate as to whether protofibrils are precursors or monomer reservoirs. We have systematically investigated the roles of time, peptide concentration, temperature, and seed size. In general, we find that there are two kinds of lag time arising from two different mechanisms. For higher temperatures or low enough concentrations close to the disassembly boundary, the fibrillization follows the nucleation mechanism. However, for low temperatures, where the nucleation time is sufficiently short, there still exists an apparent lag time due to slow Ostwald ripening mechanism. Consequently, the lag time is nonmonotonic with temperature, with the shortest lag time occurring at intermediate temperatures, which in turn depend on the peptide concentration. While the nucleation dominated regime can be controlled by seeding, the Ostwald ripening regime is insensitive to seeding. Simulation results from our coarse-grained model on the fibril size, lag time, elongation rate, and solubility are consistent with available experimental observations on many specific amyloid systems.

Deformation and failure of protein materials in physiologically extreme conditions and disease

Biological protein materials feature hierarchical structures that make up a diverse range of physiological materials. The analysis of protein materials is an emerging field that uses the relationships between biological structures, processes and properties to probe deformation and failure phenomena at the molecular and microscopic level. Here we discuss how advanced experimental, computational and theoretical methods can be used to assess structure-process-property relations and to monitor and predict mechanisms associated with failure of protein materials. Case studies are presented to examine failure phenomena in the progression of disease. From this materials science perspective, a de novo basis for understanding biological processes can be used to develop new approaches for treating medical disorders. We highlight opportunities to use knowledge gained from the integration of multiple scales with physical, biological and chemical concepts for potential applications in materials design and nanotechnology.

Replica exchange simulations of the thermodynamics of Abeta fibril growth

Replica exchange molecular dynamics and an all-atom implicit solvent model are used to probe the thermodynamics of deposition of Alzheimer's Abeta monomers on preformed amyloid fibrils. Consistent with the experiments, two deposition stages have been identified. The docking stage occurs over a wide temperature range, starting with the formation of the first peptide-fibril interactions at 500 K. Docking is completed when a peptide fully adsorbs on the fibril edge at the temperature of 380 K. The docking transition appears to be continuous, and occurs without free energy barriers or intermediates. During docking, incoming Abeta monomer adopts a disordered structure on the fibril edge. The locking stage occurs at the temperature of approximately 360 K and is characterized by the rugged free energy landscape. Locking takes place when incoming Abeta peptide forms a parallel beta-sheet structure on the fibril edge. Because the beta-sheets formed by locked Abeta peptides are typically off-registry, the structure of the locked phase differs from the structure of the fibril interior. The study also reports that binding affinities of two distinct fibril edges with respect to incoming Abeta peptides are different. The peptides bound to the concave edge have significantly lower free energy compared to those bound on the convex edge. Comparison with the available experimental data is discussed.

Self-templated nucleation in peptide and protein aggregation

Peptides and proteins exhibit a common tendency to assemble into highly ordered fibrillar aggregates, whose formation proceeds in a nucleation-dependent manner that is often preceded by the formation of oligomeric assemblies. This process has received much attention because disordered oligomeric aggregates have been associated with neurodegenerative disorders such as Alzheimer's and Parkinson's disease. Here we describe a self-templated nucleation mechanism that determines the transition between the initial condensation of polypeptide chains into disordered assemblies and their reordering into fibrillar structures. The results that we present show that at the molecular level this transition is due to the ability of polypeptide chains to reorder within oligomers into fibrillar assemblies whose surfaces act as templates that stabilize the disordered assemblies.

Formation and growth of oligomers: a Monte Carlo study of an amyloid tau fragment

Small oligomers formed early in the process of amyloid fibril formation may be the major toxic species in Alzheimer's disease. We investigate the early stages of amyloid aggregation for the tau fragment AcPHF6 (Ac-VQIVYK-NH2) using an implicit solvent all-atom model and extensive Monte Carlo simulations of 12, 24, and 36 chains. A variety of small metastable aggregates form and dissolve until an aggregate of a critical size and conformation arises. However, the stable oligomers, which are β-sheet-rich and feature many hydrophobic contacts, are not always growth-ready. The simulations indicate instead that these supercritical oligomers spend a lengthy period in equilibrium in which considerable reorganization takes place accompanied by exchange of chains with the solution. Growth competence of the stable oligomers correlates with the alignment of the strands in the β-sheets. The larger aggregates seen in our simulations are all composed of two twisted β-sheets, packed against each other with hydrophobic side chains at the sheet–sheet interface. These β-sandwiches show similarities with the proposed steric zipper structure for PHF6 fibrils but have a mixed parallel/antiparallel β-strand organization as opposed to the parallel organization found in experiments on fibrils. Interestingly, we find that the fraction of parallel β-sheet structure increases with aggregate size. We speculate that the reorganization of the β-sheets into parallel ones is an important rate-limiting step in the formation of PHF6 fibrils.

It is believed that the self association of certain protein molecules into aggregated structures, known as amyloid fibrils, plays an important role in a variety of human diseases, such as Alzheimer's disease and Parkinson's disease. Although the ability to form such amyloid fibrils is a common property for proteins, the process leading to these fibrils is incompletely understood. The early stages of the process involve small transient heterogeneous structures made of a few protein chains and are especially difficult to characterize. Here we use atomic-level simulations to explore the early part of the aggregation process for a fibril-forming fragment of the protein tau associated with Alzheimer's disease. We find that a multitude of small aggregates, rich in sheetlike structures, form through a nucleation process. Interestingly, a statistically preferred type of aggregate, consisting of two tightly packed sheets, emerges with increasing aggregate size. Growth of these larger aggregates seems to be a slow process that correlates with the emergence of more uniformly ordered sheets. We speculate that reorganization of the protein chains leading to that ordered arrangement is an important bottleneck to amyloid fibril formation for this peptide.

The Alzheimer beta-amyloid (Abeta(1-39)) dimer in an implicit solvent

Oligomers of Abeta peptides are suspected as the underlying cause of Alzheimer disease. Knowledge of their structural properties could therefore lead to a deeper understanding of the mechanism behind the outbreak of this disease. As a step in this direction we have studied Abeta dimers by all-atom molecular dynamics simulations. Equilibrated structures at 300 K were clustered into different families with similar structural features. The dominant cluster has parallel N-terminals and a well defined segment Leu17-Ala21 that are stabilized by salt bridges between Lys28 of one chain and either Glu22 or Asp23 of the other chain. The formation of these salt bridges may be the limiting step in oligomerization and fibrillogenesis.

A generic mechanism of emergence of amyloid protofilaments from disordered oligomeric aggregates

The presence of oligomeric aggregates, which is often observed during the process of amyloid formation, has recently attracted much attention because it has been associated with a range of neurodegenerative conditions including Alzheimer's and Parkinson's diseases. We provide a description of a sequence-indepedent mechanism by which polypeptide chains aggregate by forming metastable oligomeric intermediate states prior to converting into fibrillar structures. Our results illustrate that the formation of ordered arrays of hydrogen bonds drives the formation of beta-sheets within the disordered oligomeric aggregates that form early under the effect of hydrophobic forces. Individual beta-sheets initially form with random orientations and subsequently tend to align into protofilaments as their lengths increase. Our results suggest that amyloid aggregation represents an example of the Ostwald step rule of first-order phase transitions by showing that ordered cross-beta structures emerge preferentially from disordered compact dynamical intermediate assemblies.

All-atom computer simulations of amyloid fibrils disaggregation

Amyloidlike fibrils are found in many fatal diseases, including Alzheimer's disease, type II diabetes mellitus, transmissible spongiform encephalopathies, and prion diseases. These diseases are linked to proteins that have partially unfolded, misfolded, and aggregated into amyloidlike fibrils. The kinetics of amyloidlike fibrils aggregation is still hotly debated and remains an important open question. We have utilized the GNNQQNY crystal structure and high-temperature molecular dynamics simulation in explicit solvent to study the disaggregation mechanism of the GNNQQNY fibrils and to infer its likely aggregation pathways. A hexamer model and a 12-mer model both with two parallel beta-sheets separated by a dry side-chain interface were adopted in our computational analysis. A cumulative time of 1 micros was simulated for the hexamer model at five different temperatures (298 K, 348 K, 398 K, 448 K, and 498 K), and a cumulative time of 2.1 micros was simulated for the 12-mer model at four temperatures (298 K, 398 K, 448 K, and 498 K). Our disaggregation landscape and kinetics analyses indicate that tetramers probably act as the transition state in both the hexamer and the 12-mer simulations. In addition, the 12-mer simulations show that the initial aggregation nucleus is with eight peptides. Furthermore, the landscape is rather flat from 8-mers to 12-mers, indicating the absence of major barriers once the initial aggregation nucleus forms. Thus, the likely aggregation pathway is from monomers to the initial nucleus of 8-mers with tetramers as the transition state. Transition state structure analysis shows that the two dominant transition state conformations are tetramers in the 3-1 and 2-2 arrangements. The predominant nucleus conformations are in peptide arrangements maximizing dry side-chain contacts. Landscape and kinetics analyses also indicate that the parallel beta-sheets form earlier than the dry side-chain contacts during aggregation. These results provide further insights in understanding the early fibrils aggregation.

Finite size effects in simulations of protein aggregation

It is becoming increasingly clear that the soluble protofibrillar species that proceed amyloid fibril formation are associated with a range of neurodegenerative disorders such as Alzheimer's and Parkinson diseases. Computer simulations of the processes that lead to the formation of these oligomeric species are starting to make significant contributions to our understanding of the determinants of protein aggregation. We simulate different systems at constant concentration but with a different number of peptides and we study the how the finite number of proteins affects the underlying free energy of the system and therefore the relative stability of the species involved in the process. If not taken into account, this finite size effect can undermine the validity of theoretical predictions regarding the relative stability of the species involved and the rates of conversion from one to the other. We discuss the reasons that give rise to this finite size effect form both a probabilistic and energy fluctuations point of view and also how this problem can be dealt by a finite size scaling analysis.

Temperature-induced dissociation of Abeta monomers from amyloid fibril

Using all-atom molecular dynamics, we study the temperature-induced dissociation of Abeta monomers from the fibril protofilament. To accelerate conformational sampling, simulations are performed at elevated temperatures and peptide concentrations. By computing free energy disconnectivity graphs we mapped the free energy landscape of monomers on the surface of Abeta fibril. We found that Abeta monomers sample diverse sets of low free energy states with different degrees of association with the fibril. Some of these states have residual amounts of fibril interactions, whereas others lack fibril-like content. Generally, Abeta monomers with partially formed fibril-like interactions have the lowest free energies, but their backbone conformations may differ considerably from those in the fibril interior. Overall, Abeta amyloid protofilaments seem to be highly resistant to thermal dissociation. Monomer dissociation from the fibril edge proceeds via multiple stages and pathways. Our simulation findings are discussed in the context of recent experimental results.

Exploring the suitability of coarse-grained techniques for the representation of protein dynamics

A systematic study of two coarse-grained techniques for the description of protein dynamics is presented. The two techniques exploit either Brownian or discrete molecular dynamics algorithms applied in the context of simple C(alpha)-C(alpha) potentials, like those used in coarse-grained normal mode analysis. Coarse-grained simulations of the flexibility of protein metafolds are compared to those computed with fully atomistic molecular dynamics simulations using state-of-the-art physical potentials and explicit solvent. Both coarse-grained models efficiently capture critical features of the protein dynamics.

The kinetics of aggregation of poly-glutamic acid based polypeptides

The aggregation of two negatively-charged polypeptides, poly-L-glutamic acid (PE) and a copolymer of poly-glutamic acid and poly-alanine (PEA), has been studied at different peptide and salt concentrations and solution pH conditions. The kinetics of aggregation were based on Thioflavin T (ThT) fluorescence measurements. The observed lag phase shortened and the aggregation was faster as the pH approached the polypeptides' isoelectric points. While the initial polypeptide structures of PE and PEA appeared identical as determined from circular dichroism spectroscopy, the final aggregate morphology differed; PE assumed large twisted lamellar structures and the PEA formed typical amyloid-like fibrils, although both contained extensive beta-sheet structure. Differences in aggregation behavior were observed for the two polypeptides as a function of salt concentration; aggregation progressed more slowly for PE and more quickly for PEA with increasing salt concentration. Several models of aggregation kinetics were fit to the data. No model yielded consistent rate constants or a critical nucleus size. A modified nucleated polymerization model was developed based on that of Powers and Powers [E.T. Powers, D.L. Powers, The kinetics of nucleated polymerizations at high concentrations: Amyloid fibril formation near and above the "supercritical concentration", Biophys. J. 91 (2006) 122-132], which incorporated the ability of oligomeric species to interact. This provided a best fit to the experimental data.

PABPN1 polyalanine tract deletion and long expansions modify its aggregation pattern and expression

Expansions of a (GCN)10/polyalanine tract in the Poly(A) Binding Protein Nuclear 1 (PABPN1) cause autosomal dominant oculopharyngeal muscular dystrophy (OPMD). In OPMD muscles, as in models, PABPN1 accumulates in intranuclear inclusions (INIs) whereas in other diseases caused by similar polyalanine expansions, the mutated proteins have been shown to abnormally accumulate in the cytoplasm. This study presents the impact on the subcellular localization of PABPN1 produced by large expansions or deletion of its polyalanine tract. Large tracts of more than 24 alanines result in the nuclear accumulation of PABPN1 in SFRS2-positive functional speckles and a significant decline in cell survival. These large expansions do not cause INIs formation nor do they lead to cytoplasmic accumulation. Deletion of the polyalanine tract induces the formation of aggregates that are located on either side and cross the nuclear membrane, highlighting the possible role of the N-terminal polyalanine tract in PABPN1 nucleo-cytoplasmic transport. We also show that even though five other proteins with polyalanine tracts tend to aggregate when over-expressed they do not co-aggregate with PABPN1 INIs. This study presents the first experimental evidence that there may be a relative loss of function in OPMD by decreasing the availability of PABPN1 through an INI-independent mechanism.

Abeta-globulomers are formed independently of the fibril pathway

Soluble A beta-oligomers are currently discussed as the major causative species for the development of Alzheimer's disease (AD). Consequently, the beta-amyloid cascade hypothesis was extended by A beta-oligomers and their central neuropathogenic role in AD. However, the molecular structure of A beta-oligomers and their relation to amyloid fibril formation remains elusive. Previously we demonstrated that incubation of A beta(1-42) with SDS or fatty acids induces the formation of a homogeneous globular A beta-oligomer termed A beta-globulomer. In this study we investigated the role of A beta-globulomers in the aggregation pathway of A beta-peptide. We used in vitro assays such as thioflavin-T binding and aggregation inhibitors like Congo red to reveal that A beta-peptide in its A beta-globulomer conformation is a structural entity which is independent from amyloid fibril formation. In addition, cellular Alzheimer's-like plaque forming assays show the resistance of A beta-globulomers to deposition as amyloid plaques. We hypothesize that a conformational switch of A beta is decisive for either fibril formation or alternatively and independently A beta-globulomer formation.

Oscillatory molecular driving force for protein folding at high concentration: a molecular simulation

This paper presents a Langevin dynamics simulation that suggests a novel way to fold protein at high concentration, a fundamental issue in neurodegenerative diseases in vivo and the production of recombinant proteins in vitro. The simulation indicates that the folding of a coarse-grained beta-barrel protein at high concentration follows the "collapse-rearrangement" mechanism but it yields products of various forms, including single proteins in the native, misfolded, and uncollapsed forms and protein aggregates. Misfolded and uncollapased proteins are the "nucleus" of the aggregates that also encapsulate some correctly folded proteins (native proteins). An optimum hydrophobic interaction strength (epsilon*(p)) between the hydrophobic beads of the model protein, which results from a compromise between the kinetics of collapse and rearrangement, is identified for use in increasing the rate of folding over aggregating. Increased protein concentration hinders the structural transitions in both collapse and rearrangement and thus favors aggregation. A new method for protein folding at high concentration is proposed, which uses an oscillatory molecular driving force (epsilon*(p)) to promote the dissociation of aggregates in the low epsilon*(p) regime while promoting folding at a high epsilon*(p). The advantage of this method in enhancing protein folding while depressing aggregation is illustrated by a comparison with the methods based on direct dilution or applying a denaturant gradient.

Investigating the mechanism of peptide aggregation: insights from mixed monte carlo-molecular dynamics simulations

The early stages of peptide aggregation are currently not accessible by experimental techniques at atomic resolution. In this article, we address this problem through the application of a mixed simulation scheme in which a preliminary coarse-grained Monte Carlo analysis of the free-energy landscape is used to identify representative conformations of the aggregates and subsequent all-atom molecular dynamics simulations are used to analyze in detail possible pathways for the stabilization of oligomers. This protocol was applied to systems consisting of multiple copies of the model peptide GNNQQNY, whose detailed structures in the aggregated state have been recently solved in another study. The analysis of the various trajectories provides dynamical and structural insight into the details of aggregation. In particular, the simulations suggest a hierarchical mechanism characterized by the initial formation of stable parallel beta-sheet dimers and identify the formation of the polar zipper motif as a fundamental feature for the stabilization of initial oligomers. Simulation results are consistent with experimentally derived observations and provide an atomically detailed view of the putative initial stages of fibril formation.

Molecular simulation study of peptide amphiphile self-assembly

We study the self-assembly of peptide amphiphile (PA) molecules, which is governed by hydrophobic interactions between alkyl tails and a network of hydrogen bonds between peptide blocks. We demonstrate that the interplay between these two interactions results in the formation of assemblies of different morphology, in particular, single beta-sheets connected laterally by hydrogen bonds, stacks of parallel beta-sheets, spherical micelles, micelles with beta-sheets in the corona, and long cylindrical fibers. We characterize the size distribution of the aggregates as a function of the molecular interactions. Our results suggest that the formation of nanofibers of peptide amphiphiles obeys an open association model, which resembles living polymerization.

Protein folding: then and now

Over the past three decades the protein folding field has undergone monumental changes. Originally a purely academic question, how a protein folds has now become vital in understanding diseases and our abilities to rationally manipulate cellular life by engineering protein folding pathways. We review and contrast past and recent developments in the protein folding field. Specifically, we discuss the progress in our understanding of protein folding thermodynamics and kinetics, the properties of evasive intermediates, and unfolded states. We also discuss how some abnormalities in protein folding lead to protein aggregation and human diseases.

Structural reorganisation and potential toxicity of oligomeric species formed during the assembly of amyloid fibrils

Increasing evidence indicates that oligomeric protein assemblies may represent the molecular species responsible for cytotoxicity in a range of neurological disorders including Alzheimer and Parkinson diseases. We use all-atom computer simulations to reveal that the process of oligomerization can be divided into two steps. The first is characterised by a hydrophobic coalescence resulting in the formation of molten oligomers in which hydrophobic residues are sequestered away from the solvent. In the second step, the oligomers undergo a process of reorganisation driven by interchain hydrogen bonding interactions that induce the formation of beta sheet rich assemblies in which hydrophobic groups can become exposed. Our results show that the process of aggregation into either ordered or amorphous species is largely determined by a competition between the hydrophobicity of the amino acid sequence and the tendency of polypeptide chains to form arrays of hydrogen bonds. We discuss how the increase in solvent-exposed hydrophobic surface resulting from such a competition offers an explanation for recent observations concerning the cytotoxicity of oligomeric species formed prior to mature amyloid fibrils.

Effects of hydrophobic and dipole-dipole interactions on the conformational transitions of a model polypeptide

We studied the effects of hydrophobicity and dipole-dipole interactions between the nearest-neighbor amide planes on the secondary structures of a model polypeptide by calculating the free energy differences between different peptide structures. The free energy calculations were performed with low computational costs using the accelerated Monte Carlo simulation (umbrella sampling) method, with a bias-potential method used earlier in our accelerated molecular dynamics simulations. It was found that the hydrophobic interaction enhances the stability of alpha helices at both low and high temperatures but stabilizes beta structures only at high temperatures at which alpha helices are not stable. The nearest-neighbor dipole-dipole interaction stabilizes beta structures under all conditions, especially in the low temperature region where alpha helices are the stable structures. Our results indicate clearly that the dipole-dipole interaction between the nearest neighboring amide planes plays an important role in determining the peptide structures. Current research provides a more unified and quantitative picture for understanding the effects of different forms of interactions on polypeptide structures. In addition, the present model can be extended to describe DNA/RNA, polymer, copolymer, and other chain systems.

Multiscale Coarse-Graining of Monosaccharides

A systematic multiscale coarse-graining (MS-CG) algorithm is applied to build coarse-grained models for monosaccharides in aqueous solution. The methodology is demonstrated for the example of alpha-D-glucopyranose. The nonbonded interactions are directly derived from the force-matching approach, whereas the bonded interactions are obtained through Boltzmann statistical analyses of the underlying atomistic trajectory. The MS-CG model is shown to reproduce many structural and thermodynamic properties in the constant NPT ensemble. Although the model is derived at a single temperature, pressure, and concentration, it is shown to be reasonably transferable to other thermodynamic states. In this model, long-range interactions are effectively mapped into short-range forces with a moderate cutoff and are evaluated by table look-up. As a result, molecular dynamics employing the MS-CG model is approximately 3 orders of magnitude more efficient than its atomistic counterpart. Consequently, the model is particularly suitable for simulating carbohydrate systems at large length and long time scales. Results for an alpha-(1-->4)-d-glucan with 14 glucose units are also presented, demonstrating that the MS-CG algorithm is also applicable to the coarse-graining of other saccharide systems.

Mixed atomistic and coarse-grained molecular dynamics: simulation of a membrane-bound ion channel

The recently developed multiscale coarse-graining (MS-CG) method (Izvekov, S.; Voth, G. A. J. Phys. Chem. B 2005, 109, 2469; J. Chem. Phys. 2005, 123, 134105) is used to build a mixed all-atom and coarse-grained (AA-CG) model of the gramicidin A (gA) ion channel embedded in a dimyristoylphosphatidylcholine (DMPC) lipid bilayer and water environment. In this model, the gA peptide was described in full atomistic detail, while the lipid and water molecules were described using coarse-grained representations. The atom-CG and CG-CG interactions in the mixed AA-CG model were determined using the MS-CG method. Molecular dynamics (MD) simulations were performed using the resulting AA-CG model. The results from simulations of the AA-CG model compare very favorably to those from all-atom MD simulations of the entire system. Since the MS-CG method employs a general and systematic approach to obtain effective interactions from the underlying all-atom models, the present approach to rigorously develop mixed AA-CG models has the potential to be extended to many other systems.

Characterization of the nucleation barriers for protein aggregation and amyloid formation

Despite the complexity and the specificity of the amino acid code, a variety of peptides and proteins unrelated in sequence and function exhibit a common behavior and assemble into highly organized amyloid fibrils. The formation of such aggregates is often described by a nucleation and growth mechanism, in which the proteins involved also form intermediate oligomeric aggregates before they reorganize and grow into ordered fibrils with a characteristic cross-beta structure. It is extremely difficult to experimentally obtain an accurate description of the early stages of this phenomenon due to the transient nature and structural heterogeneity of the oligomeric precursors. We investigate here the phenomenon of ordered aggregation by using the recently introduced tube model of polypeptide chains in conjunction with the generic hypothesis of amyloid formation. Under conditions where oligomer formation is a rare event-the most common conditions for forming amyloid fibrils by experiment-we calculate directly the nucleation barriers associated with oligomer formation and conversion into cross-beta structure in order to reveal the nature of these species, determine the critical nuclei, and characterize their dependence on the hydrophobicity of the peptides and the thermodynamic parameters associated with aggregation and amyloid formation.

Self-assembly of β-sheet forming peptides into chiral fibrillar aggregates

The authors introduce a novel mid-resolution off-lattice coarse-grained model to investigate the self-assembly of beta-sheet forming peptides. The model retains most of the peptide backbone degrees of freedom as well as one interaction center describing the side chains. The peptide consists of a core of alternating hydrophobic and hydrophilic residues, capped by two oppositely charged residues. Nonbonded interactions are described by Lennard-Jones and Coulombic terms. The influence of different levels of "hydrophobic" and "steric" forces between the side chains of the peptides on the thermodynamics and kinetics of aggregation was investigated using Langevin dynamics. The model is simple enough to allow the simulation of systems consisting of hundreds of peptides, while remaining realistic enough to successfully lead to the formation of chiral, ordered beta tapes, ribbons, as well as higher order fibrillar aggregates.

Folding versus aggregation: polypeptide conformations on competing pathways

Protein aggregation has now become recognised as an important and generic aspect of protein energy landscapes. Since the discovery that numerous human diseases are caused by protein aggregation, the biophysical characterisation of misfolded states and their aggregation mechanisms has received increased attention. Utilising experimental techniques and computational approaches established for the analysis of protein folding reactions has ensured rapid advances in the study of pathways leading to amyloid fibrils and amyloid-related aggregates. Here we describe recent experimental and theoretical advances in the elucidation of the conformational properties of dynamic, heterogeneous and/or insoluble protein ensembles populated on complex, multidimensional protein energy landscapes. We discuss current understanding of aggregation mechanisms in this context and describe how the synergy between biochemical, biophysical and cell-biological experiments are beginning to provide detailed insights into the partitioning of non-native species between protein folding and aggregation pathways.

Folding of tandem-linked domains

One of the factors, which influences protein folding in vivo, is a linkage of protein domains into multidomain tandems. However, relatively little is known about the impact of domain connectivity on protein folding mechanisms. In this article, we use coarse grained models of proteins to explore folding of tandem-linked domains (TLD). We found TLD folding to follow two scenarios. In the first, the tandem connectivity produces relatively minor impact on folding and the mechanisms of folding of tandem-linked and single domains remain similar. The second scenario involves qualitative changes in folding mechanism because of tandem linkage. As a result, protein domains, which fold via two-state mechanism as single isolated domains, may form new stable intermediates when inserted into tandems. The new intermediates are created by topological constraints imposed by the linkers between domains. In both cases tandem linkage slows down folding. We propose that the impact of tandem connectivity can be minimized, if the terminal secondary structure elements (SSEs) are flexible. In particular, two factors appear to facilitate TLD folding: (1) the interactions between terminal SSE are poorly ordered in the folding transition state, whereas nonterminal SSE are better structured, (2) the interactions between terminal SSE are weak in the native state. We apply these findings to wild-type proteins by examining experimental phi-value data and by performing all-atom molecular dynamics simulations. We show that immunoglobulin-like domains appear to utilize the factors, which minimize the impact of tandem connectivity on their folding. Several single domain proteins, which are likely to misfold in tandems, are also identified.

Quantitative characterization of intrinsic disorder in polyglutamine: insights from analysis based on polymer theories

Intrinsically disordered proteins (IDPs) are unfolded under physiological conditions. Here we ask if archetypal IDPs in aqueous milieus are best described as swollen disordered coils in a good solvent or collapsed disordered globules in a poor solvent. To answer this question, we analyzed data from molecular simulations for a 20-residue polyglutamine peptide and concluded, in accord with experimental results, that water is a poor solvent for this system. The relevance of monomeric polyglutamine is twofold: It is an archetypal IDP sequence and its aggregation is associated with nine neurodegenerative diseases. The main advance in this work lies in our ability to make accurate assessments of solvent quality from analysis of simulations for a single, rather than multiple chain lengths. We achieved this through the proper design of simulations and analysis of order parameters that are used to describe conformational equilibria in polymer physics theories. Despite the preference for collapsed structures, we find that polyglutamine is disordered because a heterogeneous ensemble of conformations of equivalent compactness is populated at equilibrium. It is surprising that water is a poor solvent for polar polyglutamine and the question is: why? Our preliminary analysis suggests that intrabackbone interactions provide at least part of the driving force for the collapse of polyglutamine in water. We also show that dynamics for conversion between distinct conformations resemble structural relaxation in disordered, glassy systems, i.e., the energy landscape for monomeric polyglutamine is rugged. We end by discussing generalizations of our methods to quantitative studies of conformational equilibria of other low-complexity IDP sequences.

Molecular dynamics simulations on the oligomer-formation process of the GNNQQNY peptide from yeast prion protein Sup35

Oligomeric intermediates are possible cytotoxic species in diseases associated with amyloid deposits. Understanding the early steps of fibril formation at atomic details may provide useful information for the rational therapeutic design. In this study, using the heptapeptide GNNQQNY from the yeast prion-like protein Sup35 as a model system, for which a detailed atomic structure of the fibril formed has been determined by x-ray microcrystallography, we investigated its oligomer-formation process from monomer to tetramer at the atomistic level by means of a molecular dynamics simulation with explicit water. Although the number of simulations was limited, the qualitative statistical data gave some interesting results, which indicated that the oligomer formation might start from antiparallel beta-sheet-like dimers. When a new single peptide strand was added to the preformed dimers to form trimers and then tetramers, the transition time from disorder aggregates to regular ones for the parallel alignment was found to be obviously much less than for the antiparallel one. Moreover, the parallel pattern also statistically stayed longer, providing more chances for oligomer extending, although the number of parallel stack events was almost equal to antiparallel ones. Therefore, our simulations showed that new strands might prefer to extend in a parallel arrangement to form oligomers, which agrees with the microcrystal structure of the amyloid fibril formed by this peptide. In addition, analysis of the pi-pi stacking of aromatic residues showed that this type of interaction did not play an important role in giving directionality for beta-strand alignment but played a great influence on stabilizing the structures formed in the oligomer-formation process.

Structural and Pathway Complexity of β-Strand Reorganization within Aggregates of Human Transthyretin(105−115) Peptide

Interstrand conformational rearrangements of human transthyretin peptide (TTR(105-115)) within dimeric aggregates were simulated by means of molecular dynamics (MD) with implicit solvation model for a total length of 48 micros. The conformations sampled in the MD simulations were clustered to identify free energy minima without any projections of free energy surface. A connected graph was constructed with nodes (=clusters) and edges corresponding to free energy minima and transitions between nodes, respectively. This connected graph which reflects the complexity of the free energy surface was used to extract the transition disconnectivity graph, which reflects the overall free energy barriers between pairs of free energy minima but does not contain information on transition paths. The routes of transitions between important free energy minima were obtained by further processing the original graph and the MD data. We have found that both parallel and antiparallel aggregates are populated. The parallel aggregates with different alignment patterns are separated by nonnegligible free energy barriers. Multiroutes exist in the interstrand conformational reorganization. Most visited routes do not dominant the kinetics, while less visited routes contribute a little each but they are numerous and their total contributions are actually dominant. There are various kinds of reptation motions, including those through a beta-bulge, side-chain aided reptation, and flipping or rotation of a hairpin formed by one strand.

Protein aggregation in silico

Protein aggregation is a challenge to the successful manufacture of protein therapeutics; it can impose severe limitations on purification yields and compromise formulation stability. Advances in computer power, and the wealth of computational studies pertaining to protein folding, have facilitated the development of molecular simulation as a tool to investigate protein misfolding and aggregation. Here, we highlight the successes of protein aggregation studies carried out in silico, with a particular emphasis on studies related to biotechnology. To conclude, we discuss future prospects for the field, and identify several biotechnology-related problems that would benefit from molecular simulation.

Conformational Diversity of the Fibrillogenic Fusion Peptide B18 in Different Environments from Molecular Dynamics Simulations

The development of specific agents against amyloidoses requires an understanding of the conformational behavior of fibrillogenic peptides in different environments on the microscopic level. We present extensive molecular dynamics simulations of the fibrillogenic Bindin (103-120) B18 fusion peptide for several different environments: a water-trifluorethanol (TFE) mixture, pure water, aqueous buffer containing 100 mM NaCl, and a buffer-vapor interface. The peptide was studied as an isolated molecule in solution or at an interface. In the simulations, the conformational behavior of the peptide was found to strongly depend on the environment in agreement with experimental data. Overall, large portions of the peptide were unstructured. Preformed alpha-helical conformations were least stable in pure water and most stable in the water-TFE mixture and the buffer-vapor interface. In all environments, the alpha-helical conformation was most stable in the region around residues 113-116, which are mainly hydrophilic. Extended configurations in water or buffer folded into structures containing beta-sheets in agreement with data from circular dichroism spectroscopy. In buffer, the beta-sheet content was larger than in water and alpha-beta transitions were observed at elevated temperature. Beta-sheets were formed by hydrophobic residues; turns were formed by hydrophilic residues. A few typical beta-sheets that contain different residues are suggested. A B18 molecule in a strand-loop-strand conformation placed in buffer in contact with vapor was spontaneously adsorbed to the buffer-vapor interface with its hydrophobic side pointing toward the vapor phase. The adsorption induced the formation of turns at positions 108-119 and alpha-helical conformations in the region around residues 114-117. Alpha-helices were parallel to the interface plane in agreement with data from IR reflection absorption spectroscopy.

A statistical-mechanical theory of fibril formation in dilute protein solutions

We outline a theoretical treatment that describes fibril formation in dilute protein solutions. For this, we combine a theory describing self-assembly and conformational transition with a description of the lateral association of linear chains. Our statistical-mechanical model is able to predict the mean degree of polymerization and the length of the fibrils and their precursors, as well as the weight fractions of the different aggregated species in solution. We find that there appear to exist two regimes as a function of concentration, and as a function of the free energies of protein association: one in which low-molecular weight compounds dominate and one in which the fibrils do. The transition between these regimes can be quite sharp, and becomes sharper as more filaments are allowed to associate into a single fibril. The fraction of fibrils consisting of less than the maximum allowed number of filaments turns out to be negligible, in agreement with experimental studies, where the fibril thickness is found to be practically monodisperse. In addition, we find that the description of the fibril ends has a large effect on the predicted fibril length.

Dissociation of Abeta(16-22) amyloid fibrils probed by molecular dynamics

The mechanisms of deposition and dissociation are implicated in the assembly of amyloid fibrils. To investigate the kinetics of unbinding of Abeta(16-22) monomers from preformed fibrils, we use molecular dynamics (MD) simulations and the structures for Abeta(16-22) amyloid fibrils. Consistent with experimental studies, the dissociation of Abeta(16-22) peptides involves two main stages, locked and docked, after which peptides unbind. The lifetime of the locked state, in which a peptide retains fibril-like structure and interactions, extends up to 0.5 micros under normal physiological conditions. Upon cooperative rupture of all fibril-like hydrogen bonds (HBs) with the fibril, a peptide enters a docked state. This state is populated by disordered random coil conformations and its lifetime ranges from approximately 10 to 200 ns. The docked state is stabilized by hydrophobic side chain interactions, while the contribution from HBs is small. Our simulations also suggest that the peptides located on fibril edges may form stable beta-strand conformations distinct from the fibril "bulk". We propose that such edge peptides can act as fibril caps, which impede fibril elongation. Our results indicate that the interactions between unbinding peptides constitute the molecular basis for cooperativity of peptide dissociation. The kinetics of fibril growth is reconstructed from unbinding assuming the reversibility of deposition/dissociation pathways. The relation of in silica dissociation kinetics to experimental observations is discussed.

A three-stage kinetic model of amyloid fibrillation

Amyloid fibrillation has been intensively studied because of its association with various neurological disorders. While extensive time-dependent fibrillation experimental data are available and appear similar, few mechanistic models have been developed to unify those results. The aim of this work was to interpret these experimental results via a rigorous mathematical model that incorporates the physical chemistry of nucleation and fibril growth dynamics. A three-stage mechanism consisting of protein misfolding, nucleation, and fibril elongation is proposed and supported by the features of homogeneous fibrillation responses. Estimated by nonlinear least-squares algorithms, the rate constants for nucleation were approximately 10,000,000 times smaller than those for fibril growth. These results, coupled with the positive feedback characteristics of the elongation process, account for the typical sigmoidal behavior during fibrillation. In addition, experiments with different proteins, various initial concentrations, seeding versus nonseeding, and several agitation rates were analyzed with respect to fibrillation using our new model. The wide applicability of the model confirms that fibrillation kinetics may be fairly similar among amyloid proteins and for different environmental factors. Recommendations on further experiments and on the possible use of molecular simulations to determine the desired properties of potential fibrillation inhibitors are offered.

Hydrophobic cooperativity as a mechanism for amyloid nucleation

The kinetics of amyloid fibril formation are in most cases explained by classical nucleation theory, yet the mechanisms behind nucleation are not well understood. We show using molecular dynamics simulations that the hydrophobic cooperativity in the self-association of the model amyloidogenic peptide STVIYE is sufficient to allow for nucleation-dependent polymerization with a pentamer critical nucleus. The role of electrostatics was also investigated. Novel considerations of the electrostatic solvation energy using the Born-Onsager equation are put forth to rationalize the aggregation of charged peptides and provide new insight into the energetic differences between parallel and antiparallel beta-sheets. Together these results help explain the influence of molecular charge in the class of fibril-forming hexapeptides recently designed by Serrano and collaborators.

Aggregating the amyloid Abeta(11-25) peptide into a four-stranded beta-sheet structure

We present a detailed analysis of the structural properties of one monomer of Abeta(11-25) as well as of the aggregation mechanisms for four chains of Abeta(11-25) using the activation-relaxation technique coupled with a generic energy potential. Starting from a random distribution of these four chains, we find that the system assembles rapidly into a random globular state that evolves into three- and four-stranded antiparallel beta-sheets. The aggregation process is considerably accelerated by the presence of preformed dimers. We also find that the reptation mechanism already identified in shorter peptides plays a significant role here in allowing the structure to reorganize without having to fully dissociate.

Effects of chain length on the aggregation of model polyglutamine peptides: molecular dynamics simulations

Aggregation in the brain of polyglutamine-containing proteins is either a cause or an associated symptom of nine hereditary neurodegenerative disorders including Huntington's disease. The molecular level mechanisms by which these proteins aggregate are still unclear. In an effort to shed light on this important phenomenon, we are investigating the aggregation of model polyglutamine peptides using molecular-level computer simulation with a simplified model of polyglutamine that we have developed. This model accounts for the most important types of intra- and inter-molecular interactions-hydrogen bonding and hydrophobic interactions-while allowing the folding process to be simulated in a reasonable time frame. The model is used to examine the folding of isolated polyglutamine peptides 16, 32, and 48 residues long and the folding and aggregation of systems of 24 model polyglutamine peptides 16, 24, 32, 36, 40, and 48 residues long. Although the isolated polyglutamine peptides did form some alpha and beta backbone-backbone hydrogen bonds they did not have as many of these bonds as they would have if they had folded into a complete alpha helix or beta sheet. In one of the simulations on the isolated polyglutamine peptide 48 residues long, we observed a structure that resembles a beta helix. In the multi-chain simulations we observed amorphous aggregates at low temperatures, ordered aggregates with significant beta sheet character at intermediate temperatures, and random coils at high temperatures. We have found that the temperature at which the model peptides undergo the transition from amorphous aggregates to ordered aggregates and the temperature at which the model peptides undergo the transition from ordered aggregates to random coils increase with increasing chain length. Our finding that the stability of the ordered aggregates increases as the peptide chain length increases may help to explain the experimentally observed relation between polyglutamine tract length and aggregation in vitro and disease progression in vivo. We have also observed in our simulations that the optimal temperature for the formation of beta sheets increases with chain length up to 36 glutamine residues but not beyond. Equivalently, at fixed temperature we find a transition from a region dominated by random coils at chain lengths less than 36 to a region dominated by relatively ordered beta sheet structures at chain lengths greater than 36. Our finding of this critical chain length of 36 glutamine residues is interesting because a critical chain length of 37 glutamine residues has been observed experimentally.