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

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.

Probing amyloid fibril formation of the NFGAIL peptide by computer simulations

Amyloid fibril formation, as observed in Alzheimer's disease and type II diabetes, is currently described by a nucleation-condensation mechanism, but the details of the process preceding the formation of the nucleus are still lacking. In this study, using an activation-relaxation technique coupled to a generic energy model, we explore the aggregation pathways of 12 chains of the hexapeptide NFGAIL. The simulations show, starting from a preformed parallel dimer and ten disordered chains, that the peptides form essentially amorphous oligomers or more rarely ordered beta-sheet structures where the peptides adopt a parallel orientation within the sheets. Comparison between the simulations indicates that a dimer is not a sufficient seed for avoiding amorphous aggregates and that there is a critical threshold in the number of connections between the chains above which exploration of amorphous aggregates is preferred.

Structure and dynamics of parallel beta-sheets, hydrophobic core, and loops in Alzheimer's A beta fibrils

We explore the relative contributions of different structural elements to the stability of Abeta fibrils by molecular-dynamics simulations performed over a broad range of temperatures (298 K to 398 K). Our fibril structures are based on solid-state nuclear magnetic resonance experiments of Abeta(1-40) peptides, with sheets of parallel beta-strands connected by loops and stabilized by interior salt bridges. We consider models with different interpeptide interfaces, and different staggering of the N- and C-terminal beta-strands along the fibril axis. Multiple 10-20 ns molecular-dynamics simulations show that fibril segments with 12 peptides are stable at ambient temperature. The different models converge toward an interdigitated side-chain packing, and present water channels solvating the interior D23/K28 salt bridges. At elevated temperatures, we observe the early phases of fibril dissociation as a loss of order in the hydrophilic loops connecting the two beta-strands, and in the solvent-exposed N-terminal beta-sheets. As the most dramatic structural change, we observe collective sliding of the N- and C-terminal beta-sheets on top of each other. The interior C-terminal beta-sheets in the hydrophobic core remain largely intact, indicating that their formation and stability is crucial to the dissociation/elongation and stability of Abeta fibrils.

Protein misfolding, functional amyloid, and human disease

Peptides or proteins convert under some conditions from their soluble forms into highly ordered fibrillar aggregates. Such transitions can give rise to pathological conditions ranging from neurodegenerative disorders to systemic amyloidoses. In this review, we identify the diseases known to be associated with formation of fibrillar aggregates and the specific peptides and proteins involved in each case. We describe, in addition, that living organisms can take advantage of the inherent ability of proteins to form such structures to generate novel and diverse biological functions. We review recent advances toward the elucidation of the structures of amyloid fibrils and the mechanisms of their formation at a molecular level. Finally, we discuss the relative importance of the common main-chain and side-chain interactions in determining the propensities of proteins to aggregate and describe some of the evidence that the oligomeric fibril precursors are the primary origins of pathological behavior.

Thermodynamics of folding and association of lattice-model proteins

Closely related to the "protein folding problem" is the issue of protein misfolding and aggregation. Protein aggregation has been associated with the pathologies of nearly 20 human diseases and presents serious difficulties during the manufacture of pharmaceutical proteins. Computational studies of multiprotein systems have recently emerged as a powerful complement to experimental efforts aimed at understanding the mechanisms of protein aggregation. We describe the thermodynamics of systems containing two lattice-model 64-mers. A parallel tempering algorithm abates problems associated with glassy systems and the weighted histogram analysis method improves statistical quality. The presence of a second chain has a substantial effect on single-chain conformational preferences. The melting temperature is substantially reduced, and the increase in the population of unfolded states is correlated with an increase in interactions between chains. The transition from two native chains to a non-native aggregate is entropically favorable. Non-native aggregates receive approximately 25% of their stabilizing energy from intraprotein contacts not found in the lowest-energy structure. Contact maps show that for non-native dimers, nearly 50% of the most probable interprotein contacts involve pairs of residues that form native contacts, suggesting that a domain-swapping mechanism is involved in self-association.

Following the aggregation of amyloid-forming peptides by computer simulations

There is experimental evidence suggesting that the toxicity of neurodegenerative diseases such as Alzheimer's disease may result from the soluble intermediate oligomers. It is therefore important to characterize extensively the early steps of oligomer formation at atomic level. As these structures are metastable and short lived, experimental data are difficult to obtain and they must be complemented with numerical simulations. In this work, we use the activation-relaxation technique coupled with a coarse-grained energy model to study in detail the mechanisms of aggregation of four lys-phe-phe-glu (KFFE) peptides. This is the shortest peptide known to form amyloid fibrils in vitro. Our simulations indicate that four KFFE peptides adopt a variety of oligomeric states (tetramers, trimers, and dimers) with various orientations of the chains in rapid equilibrium. This conformational distribution is consistent with all-atom molecular-dynamics simulations in explicit solvent and is sequence dependent; as seen experimentally, the lys-pro-gly-glu (KPGE) peptides adopt disordered structures in solution. Our unbiased simulations also indicate that the assembly process is much more complex than previously thought and point to intermediate structures which likely are kinetic traps for longer chains.

Coarse-grained protein molecular dynamics simulations

A limiting factor in biological science is the time-scale gap between experimental and computational trajectories. At this point, all-atom explicit solvent molecular dynamics (MD) are clearly too expensive to explore long-range protein motions and extract accurate thermodynamics of proteins in isolated or multimeric forms. To reach the appropriate time scale, we must then resort to coarse graining. Here we couple the coarse-grained OPEP model, which has already been used with activated methods, to MD simulations. Two test cases are studied: the stability of three proteins around their experimental structures and the aggregation mechanisms of the Alzheimer's Abeta16-22 peptides. We find that coarse-grained isolated proteins are stable at room temperature within 50 ns time scale. Based on two 220 ns trajectories starting from disordered chains, we find that four Abeta16-22 peptides can form a three-stranded beta sheet. We also demonstrate that the reptation move of one chain over the others, first observed using the activation-relaxation technique, is a kinetically important mechanism during aggregation. These results show that MD-OPEP is a particularly appropriate tool to study qualitatively the dynamics of long biological processes and the thermodynamics of molecular assemblies.

Computational simulations of the early steps of protein aggregation

There is strong evidence that the oligomers of key proteins, formed during the early steps of aggregation, could be the primary toxic species associated with human neuro-degenerative diseases, such as Alzheimer's and prion diseases. Here, we review recent progress in the development of computational approaches in order to understand the structures, dynamics and free energy surfaces of oligomers. We also discuss possible research directions for the coming years.

Molecular dynamics simulation suggests possible interaction patterns at early steps of beta2-microglobulin aggregation

Early events in aggregation of proteins are not easily accessible by experiments. In this work, we perform a 5-ns molecular dynamics simulation of an ensemble of 27 copies of beta(2)-microglobulin in explicit solvent. During the simulation, the formation of intermolecular contacts is observed. The simulation highlights the importance of apical residues and, in particular, of those at the N-terminus end of the molecule. The most frequently found pattern of interaction involves a head-to-head contact arrangement of molecules. Hydrophobic contacts appear to be important for the establishment of long-lived (on the simulation timescale) contacts. Although early events on the pathway to aggregation and fibril formation are not directly related to the end-state of the process, which is reached on a much longer timescale, simulation results are consistent with experimental data and in general with a parallel arrangement of intermolecular beta-strand pairs.

pH-dependent self-assembly of polyalanine peptides

Polyalanine expansions in the nuclear RNA-binding protein PABP2 induce misfolding and aggregation of the protein into insoluble inclusions in muscle tissues and cell nuclei, leading to the disease oculopharyngeal muscular dystrophy (OPMD). We have explored the effect of solvent conditions and alanine repeat number on the propensity of fibril formation in this protein deposition disease. Three peptides mimicking the N-terminal polyalanine segment of PABP2, having the generic sequence Ac-Lys-Met-(Ala)(n)-Gly-Tyr with n = 7, 11, and 17 (referred to as 7-ala, 11-ala, and 17-ala, respectively), were synthesized and their conformational properties studied as a function of pH. In strongly alkaline medium (pH >10), the two longer peptides (11-ala and 17-ala, but not 7-ala) showed remarkable enhancement of beta-sheet content and formed fibrils after incubation for 1-2 weeks at room temperature. Fluorescence studies suggested that tyrosyl radicals produced at high pH cross-linked to form dityrosine, which provided added stabilization for fibril growth. The kinetic progress curves for fibril formation, obtained by ThT fluorescence assay, showed exponential increase with time after an initial quiescent period (lag time) and an eventual saturation phase, all of which are indicative of a nucleation-controlled polymerization mechanism for fibrillation. Hierarchical self-assembly of the peptides led to the formation of striking fractal-shaped growth patterns on substrates, raising the possibility of designing novel materials using these peptides.

Structures of soluble amyloid oligomers from computer simulations

Alzheimer's, Parkinson's, and Creutzfeldt-Jakob's neurodegenerative diseases are all linked with the assembly of normally soluble proteins into amyloid fibrils. Because of experimental limitations, structural characterization of the soluble oligomers, which form early in the process of fibrillogenesis and are cytotoxic, remains to be determined. In this article, we study the aggregation paths of seven chains of the shortest amyloid-forming peptide, using an activitated method and a reduced atomic representation. Our simulations show that disordered KFFE monomers ultimately form three distinct topologies of similar energy: amorphous oligomers, incomplete rings with beta-barrel character, and cross-beta-sheet structures with the meridional but not the equatorial X-ray fiber reflections. The simulations also shed light on the pathways from misfolded aggregates to fibrillar-like structures. They also underline the multiplicity of building blocks that can lead to the formation of the critical nucleus from which rapid growth of the fibril occurs.

Interpreting the Aggregation Kinetics of Amyloid Peptides

Amyloid fibrils are insoluble mainly beta-sheet aggregates of proteins or peptides. The multi-step process of amyloid aggregation is one of the major research topics in structural biology and biophysics because of its relevance in protein misfolding diseases like Alzheimer's, Parkinson's, Creutzfeld-Jacob's, and type II diabetes. Yet, the detailed mechanism of oligomer formation and the influence of protein stability on the aggregation kinetics are still matters of debate. Here a coarse-grained model of an amphipathic polypeptide, characterized by a free energy profile with distinct amyloid-competent (i.e. beta-prone) and amyloid-protected states, is used to investigate the kinetics of aggregation and the pathways of fibril formation. The simulation results suggest that by simply increasing the relative stability of the beta-prone state of the polypeptide, disordered aggregation changes into fibrillogenesis with the presence of oligomeric on-pathway intermediates, and finally without intermediates in the case of a very stable beta-prone state. The minimal-size aggregate able to form a fibril is generated by collisions of oligomers or monomers for polypeptides with unstable or stable beta-prone state, respectively. The simulation results provide a basis for understanding the wide range of amyloid-aggregation mechanisms observed in peptides and proteins. Moreover, they allow us to interpret at a molecular level the much faster kinetics of assembly of a recently discovered functional amyloid with respect to the very slow pathological aggregation.

Different conformations of amyloid beta induce neurotoxicity by distinct mechanisms in human cortical neurons

Characterization of soluble oligomeric amyloid beta (Abeta) species in the brains of Alzheimer's disease (AD) patients and transgenic models has raised the possibility that different conformations of Abeta may contribute to AD pathology via different mechanisms. To characterize the toxic effect of different Abeta conformations, we tested side by side the effect of well characterized Abeta oligomers (AbetaOs), Abeta-derived diffusible ligands (ADDLs), and fibrillar Abeta (Abetaf) preparations in human cortical neurons (HCNs). Both AbetaOs and ADDLs bind rapidly and with high affinity to synaptic contacts and cellular membranes. AbetaOs (5 microm) induced rapid and massive neuronal death. Calcium influx accelerated, but was not required for, AbetaO toxicity. AbetaOs elicited a stereotyped succession of cellular changes consistent with the activation of a mitochondrial death apoptotic pathway. At low concentrations AbetaOs caused chronic and subtler mitochondrial alterations but minimal cell death. ADDLs induced similar toxic changes as AbetaOs but on a fivefold longer time scale. Higher concentrations of Abetaf and longer incubation times were required to produce widespread neuritic dystrophy but modest HCN cell death. Thus various Abeta species may play relevant roles in AD, causing neurotoxicity by distinct non-overlapping mechanisms affecting neuronal function and viability over multiple time courses.

Spontaneous formation of annular structures observed in molecular dynamics simulations of polyglutamine peptides

Annular structures have been observed experimentally in aggregates of polyglutamine-containing proteins and other proteins associated with diseases of the brain. Here we report the observation of annular structures in molecular-level simulations of large systems of model polyglutamine peptides. A system of 24 polyglutamine chains 16 residues long at a concentration of 5 mM spontaneously formed large beta sheets which curved to form tube-like annular structures that resemble beta barrels. This work was accomplished by extending the PRIME model to polyglutamine. PRIME is an off-lattice, unbiased, intermediate-resolution protein model based on an amino acid representation of between three and seven united atoms depending on the residue being modeled. Our results are interesting not only because of the recent discovery of tubular protofibrils in experiments on aggregation of mutant huntingtin fragments containing expanded polyglutamine tracts but also because Perutz predicted that polyglutamine forms water filled nanotubes.

Structural stability and dynamics of an amyloid-forming peptide GNNQQNY from the yeast prion sup-35

A seven amino acid yeast prion sup-35 fragment (GNNQQNY) forms amyloid fibrils. The availability of its detailed atomic oligomeric structure makes it a good model for studying the early stage of aggregation. Here we perform long all-atom explicit solvent molecular simulations of various sizes and arrangements of oligomer seeds of the wild-type and its mutants to study its stability and dynamics. Previous studies have suggested that the early stage rate-limiting step of oligomer formation occurs in high-order oligomers. Our simulations show that with the increase in the number of strands even from a dimer to a trimer, oligomer stability increases dramatically. This suggests that the minimal nucleus seed for GNNQQNY fibril formation could be small and is likely three or four peptides, in agreement with experiment, and that higher-order oligomers do not dissociate quickly since they have small diffusion coefficients and thus slow kinetics. Further, for the hydrophilic polar GNNQQNY, there are no hydrogen bonds and no hydrophobic interactions between adjacent beta-sheets. Simulations suggest that within the sheet, the driving forces to associate and stabilize are interstrand backbone-backbone and side chain-side chain hydrogen bonds, whereas between the sheets, shape-complementary by the dry polar steric zipper via the side chains of Asn-2, Gln-4, and Asn-6 holds the sheets together, as proposed in an earlier study. Since the polar side chains of Asn-2, Gln-4, and Asn-6 act as a hook to bind two neighboring sheets together, these geometric restraints reduce the conformational search for the correct side chain packing to a two-dimensional problem of intersheet side chain interactions. Mutant simulations show that substitution of Asn-2, Gln-4, or Asn-6 by Ala would disrupt this steric zipper, leading to unstable oligomers.

Mapping all-atom models onto one-bead Coarse Grained Models: general properties and applications to a minimal polypeptide model

In the one and two beads Coarse Grained (CG) models for proteins, the two conformational dihedrals ϕ and ψ that describe the backbone geometry are no longer present as explicit internal coordinates, thus the information contained in the Ramachandran plot cannot be used directly. We derive an analytical mapping between these dihedrals and the internal variable describing the backbone conformation in the one(two) beads CG models, namely the pseudo-bond angle and pseudo-dihedral between subsequent Cαs. This is used to derive a new density plot that contains the same information as the Ramachandran plot and can be used with the one(two) beads CG models. The use of this mapping is then illustrated with a new one bead polypeptide model that accounts for transitions between α-helices and β-sheets.

Effect of single-point sequence alterations on the aggregation propensity of a model protein

Sequences of contemporary proteins are believed to have evolved through a process that optimized their overall fitness, including their resistance to deleterious aggregation. Biotechnological processing may expose therapeutic proteins to conditions that are much more conducive to aggregation than those encountered in a cellular environment. An important task of protein engineering is to identify alternative sequences that would protect proteins when processed at high concentrations without altering their native structure associated with specific biological function. Our computational studies exploit parallel tempering simulations of coarse-grained model proteins to demonstrate that isolated amino acid residue substitutions can result in significant changes in the aggregation resistance of the protein in a crowded environment while retaining protein structure in isolation. A thermodynamic analysis of protein clusters subject to competing processes of folding and association shows that moderate mutations can produce effects similar to those caused by changes in system conditions, including temperature, concentration, and solvent composition, that affect the aggregation propensity. The range of conditions where a protein can resist aggregation can therefore be tuned by sequence alterations, although the protein generally may retain its generic ability for aggregation.

Side-chain interactions determine amyloid formation by model polyglutamine peptides in molecular dynamics simulations

The pathological manifestation of nine hereditary neurodegenerative diseases is the presence within the brain of aggregates of disease-specific proteins that contain polyglutamine tracts longer than a critical length. To improve our understanding of the processes by which polyglutamine-containing proteins misfold and aggregate, we have conducted molecular dynamics simulations of the aggregation of model polyglutamine peptides. This work was accomplished by extending the PRIME model to polyglutamine. PRIME is an off-lattice, unbiased, intermediate-resolution protein model based on an amino acid representation of between three and seven united atoms, depending on the residue being modeled. The effects of hydrophobicity on the system are studied by varying the strength of the hydrophobic interaction from 12.5% to 5% of the hydrogen-bonding interaction strength. In our simulations, we observe the spontaneous formation of aggregates and annular structures that are made up of beta-sheets starting from random configurations of random coils. This result was interesting because tubular protofibrils were recently found in experiments on polyglutamine aggregation and because of Perutz's prediction that polyglutamine would form water-filled nanotubes.

Coarse-grained strategy for modeling protein stability in concentrated solutions. II: phase behavior

We use highly efficient transition-matrix Monte Carlo simulations to determine equilibrium unfolding curves and fluid phase boundaries for solutions of coarse-grained globular proteins. The model we analyze derives the intrinsic stability of the native state and protein-protein interactions from basic information about protein sequence using heteropolymer collapse theory. It predicts that solutions of low hydrophobicity proteins generally exhibit a single liquid phase near their midpoint temperatures for unfolding, while solutions of proteins with high sequence hydrophobicity display the type of temperature-inverted, liquid-liquid transition associated with aggregation processes of proteins and other amphiphilic molecules. The phase transition occurring in solutions of the most hydrophobic protein we study extends below the unfolding curve, creating an immiscibility gap between a dilute, mostly native phase and a concentrated, mostly denatured phase. The results are qualitatively consistent with the solution behavior of hemoglobin (HbA) and its sickle variant (HbS), and they suggest that a liquid-liquid transition resulting in significant protein denaturation should generally be expected on the phase diagram of high-hydrophobicity protein solutions. The concentration fluctuations associated with this transition could be a driving force for the nonnative aggregation that can occur below the midpoint temperature.

Spontaneous fibril formation by polyalanines; discontinuous molecular dynamics simulations

Fibrillary protein aggregates rich in beta-sheet structure have been implicated in the pathology of several neurodegenerative diseases. In this work, we investigate the formation of fibrils by performing discontinuous molecular dynamics simulations on systems containing 12 to 96 model Ac-KA(14)K-NH(2) peptides using our newly developed off-lattice, implicit-solvent, intermediate-resolution model, PRIME. We find that, at a low concentration, random-coil peptides assemble into alpha-helices at low temperatures. At intermediate concentrations, random-coil peptides assemble into alpha-helices at low temperatures and large beta-sheet structures at high temperatures. At high concentrations, the system forms beta-sheets over a wide range of temperatures. These assemble into fibrils above a critical temperature which decreases with concentration and exceeds the isolated peptide's folding temperature. At very high temperatures and all concentrations, the system is in a random-coil state. All of these results are in good qualitative agreement with those by Blondelle and co-workers on Ac-KA(14)K-NH(2) peptides. The fibrils observed in our simulations mimic the structural characteristics observed in experiments in terms of the number of sheets formed, the values of the intra- and intersheet separations, and the parallel peptide arrangement within each beta-sheet. Finally, we find that when the strength of the hydrophobic interaction between nonpolar side chains is high compared to the strength of hydrogen bonding, amorphous aggregates, rather than fibrillar aggregates, are formed.

Improving solubility of Shewanella oneidensis MR-1 and Clostridium thermocellum JW-20 proteins expressed into Esherichia coli

Low solubility of proteins overexpressed in E. coli is a frequent problem in high-throughput structural genomics. To improve solubility of proteins from mesophilic Shewanella oneidensis MR-1 and thermophilic Clostridium thermocellum JW20, an approach was attempted that included a fusion of the target protein to a maltose-binding protein (MBP) and a decrease of induction temperature. The MBP was selected as the most efficient solubilizing carrier when compared to a glutathione S-transferase and a Nus A protein. A tobacco etch virus (TEV) protease recognition site was introduced between fused proteins using a double polymerase-chain reaction and four primers. In this way, 79 S. oneidensis proteins have been expressed in one case with an N-terminal 30-residue tag and in another case as a fusion protein with MBP. A foreign tag might significantly affect the properties of the target polypeptide. At 37 degrees C and 18 degrees C induction temperatures, only 5 and 17 tagged proteins were soluble, respectively. In fusion with MBP 4, 34, and 38 proteins were soluble upon induction at 37 degrees, 28 degrees, and 18 degrees C, respectively. The MBP is assumed to increase stability and solubility of a target protein by changing both the mechanism and the cooperativity of folding/unfolding. The 66 C. thermocellum proteins were expressed as fusion proteins with MBP. Induction at 37 degrees, 28 degrees, and 18 degrees C produced 34, 57, and 60 soluble proteins, respectively. The higher solubility of C. thermocellum proteins in comparison with the S. oneidensis proteins under similar conditions of induction correlates with the thermophilicity of the host. The two-factor Wilkinson-Harrison statistical model was used to identify soluble and insoluble proteins. Theoretical and experimental data showed good agreement for S. oneidensis proteins; however, the model failed to identify soluble/insoluble Clostridium proteins. A suggestion has been made that the Wilkinson-Harrison model is not applicable to C. thermocellum proteins because it did not account for the peculiarities of protein sequences from thermophiles.

Molecular simulation of protein aggregation

Computer simulation offers unique possibilities for investigating molecular-level phenomena difficult to probe experimentally. Drawing from a wealth of studies concerning protein folding, computational studies of protein aggregation are emerging. These studies have been successful in capturing aspects of aggregation known from experiment and are being used to refine experimental methods aimed at abating aggregation. Here we review molecular-simulation studies of protein aggregation conducted in our laboratory. Specific attention is devoted to issues with implications for biotechnology.

Ab initio discrete molecular dynamics approach to protein folding and aggregation

Understanding the toxicity of amyloidogenic protein aggregates and designing therapeutic approaches require the knowledge of their structure at atomic resolution. Although solid-state NMR, X-ray diffraction, and other experimental techniques are capable of discerning the protein fibrillar structure, determining the structures of early aggregates, called oligomers, is a challenging experimental task. Computational studies by all-atom molecular dynamics, which provides a complete description of a protein in the solvent, are typically limited to study folding of smaller protein or aggregation of a small number of short protein fragments. We review an efficient ab initio computer simulation approach to protein folding and aggregation using discrete molecular dynamics (DMD) in combination with several coarse-grained protein models and implicit solvent. This approach involves different complexity levels in both the protein model and the interparticle interactions. Starting from the simplest protein model with minimal interactions, and gradually increasing its complexity, while guided by in vitro findings, we can systematically select the key features of the protein model and interactions that drive protein folding and aggregation. Because the method used in this DMD approach does not require any knowledge of the native or any other state of the protein, it can be applied to study degenerative disorders associated with protein misfolding and aberrant protein aggregation. The choice of the coarse-grained model depends on the complexity of the protein and specific questions to be addressed, which are mostly suggested by in vitro findings. Thus, we illustrate our approach on amyloid beta-protein (Abeta) associated with Alzheimer's disease (AD). Despite the simplifications introduced in the DMD approach, the predicted Abeta conformations are in agreement with existing experimental data. The in silico findings also provide further insights into the structure and dynamics of Abeta folding and oligomer formation that are amenable to in vitro testing.

Computational approaches to fibril structure and formation

Assembly of normally soluble proteins into amyloid fibrils is a cause or associated symptom of numerous human disorders. Although some progress toward understanding the molecular-level details of fibril structure has been made through in vitro experiments, the insoluble nature of fibrils make them difficult to study experimentally. We describe two computational approaches used to investigate fibril formation and structure: intermediate-resolution discontinuous molecular dynamics simulations and atomistic molecular dynamics simulations. Each method has its strengths and weaknesses, but taken together the two approaches provide a useful molecular-level picture of fibril structure and formation.

Molecular dynamics simulations and free energy analyses on the dimer formation of an amyloidogenic heptapeptide from human beta2-microglobulin: implication for the protofibril structure

Amyloid formation is associated with many neurodegenerative diseases. Recent findings suggest that early oligomeric aggregates could be major sources of toxicity. We present a computational investigation of the first step of amyloid initiation-dimer formation of a seven residue peptide (NHVTLSQ) from human beta2-microglobulin at pH 2.0, which renders +2.0 units charges to each peptide. A total of over 1.2 micros of simulations with explicit solvent and 1.0 micros of simulations with implicit solvent were conducted. Main-chain conformational restraint was applied to facilitate the formation of ordered dimers. An antiparallel beta-sheet with six main-chain hydrogen bonds was dominant in the implicit solvent simulations. In contrast, no stable dimers were observed in the two negative controls, the mouse heptapeptide (KHDSMAE, +3.0 units charges) and the scrambled human heptapeptide (QVLHTSN). Explicit solvent simulations presented a more complex scenario. The wild-type human heptapeptide formed predominantly antiparallel beta-sheets ( approximately 38%) although parallel ones ( approximately 12%) were also observed. Hydrophobic contacts preceded hydrogen bond saturation in the majority of the association events in the explicit solvent simulations, highlighting the important role of hydrophobic interaction in amyloid initiation. The fact that the mouse dimer dissociated immediately after the removal of conformational restraint suggests that the higher conformational entropy barrier, along with the stronger charge repulsion and weaker hydrophobic interaction, contributed to its inability to form amyloid fibril. The closeness of positive charge pairs in the dimers of the scrambled human heptapeptide may prohibit further beta-sheet extension and fibril growth. Combining the results from simulations and free energy analyses, we propose that the building block for this amyloid fibril is an antiparallel dimer with a two-residue register shift and six main-chain hydrogen bonds. A double-layer protofibril structure is also proposed in which two antiparallel beta-sheets face each other and are held together by hydrophobic staples and hydrogen bonds of the polar side-chains.

Simple but predictive protein models

The traditional approach to computational biophysics studies of molecular systems is brute force molecular dynamics simulations under the conditions of interest. The disadvantages of this approach are that the time and length scales that are accessible to computer simulations often do not reach biologically relevant scales. An alternative approach, which we call intuitive modeling, is hypothesis-driven and based on tailoring simplified protein models to the systems of interest. Using intuitive modeling, the length and time scales that can be achieved using simplified protein models exceed those of traditional molecular-dynamic simulations. Here, we describe several recent studies that signify the predictive power of simplified protein models within the intuitive-modeling approach.

The Yin and Yang of protein folding

The study of protein aggregation saw a renaissance in the last decade, when it was discovered that aggregation is the cause of several human diseases, making this field of research one of the most exciting frontiers in science today. Building on knowledge about protein folding energy landscapes, determined using an array of biophysical methods, theory and simulation, new light is now being shed on some of the key questions in protein-misfolding diseases. This review will focus on the mechanisms of protein folding and amyloid fibril formation, concentrating on the role of partially folded states in these processes, the complexity of the free energy landscape, and the potentials for the development of future therapeutic strategies based on a full biophysical description of the combined folding and aggregation free-energy surface.

The other trinucleotide repeat: polyalanine expansion disorders

Expansions of trinucleotide repeats encoding polyalanine tracts have been recognized as the cause of several diseases, predominantly congenital malformation syndromes. To date, nine genes with alanine tract expansions have been described. With the exception of PABPN1, which codes for a poly(A)-binding protein, all these genes encode transcription factors that play important roles during development. Recent in vitro and in vivo findings indicate that expansions of polyalanine tracts beyond a certain threshold result in protein misfolding, aggregation and subsequent degradation. Polyalanine tracts are relatively common in the genome and occur most frequently in transcription factors and other proteins with nuclear localization. The molecular role of alanine tracts is unknown, but their strong evolutionary conservation suggests the existence of potent functional or structural constraints.

Impaired exercise capacity, but unaltered mitochondrial respiration in skeletal or cardiac muscle of mice lacking cellular prion protein

The studies of physiological roles for cellular prion protein (PrP(c)) have focused on possible functions of this protein in the CNS, where it is largely expressed. However, the observation that PrP(c) is expressed also in muscle tissue suggests that the physiological role of PrP(c) might not be limited to the central nervous system. In the present study, we investigated possible functions of PrP(c) in muscle using PrP(c) gene (Prnp) null mice (Prnp(0/0)). For this purpose, we submitted Prnp(0/0) animals to different protocols of exercise, and compared their performance to that of their respective wild-type controls. Prnp(0/0) mice showed an exercise-dependent impairment of locomotor activity. In searching for possible mechanisms associated with the impairment observed, we evaluated mitochondrial respiration (MR) in skeletal or cardiac muscle from these mice during resting or after different intensities of exercise. Baseline MR (states 3 and 4), respiratory control ratio (RCR) and mitochondrial membrane potential (DeltaPsi) were evaluated and were not different in skeletal or cardiac muscle tissue of Prnp(0/0) mice when compared with wild-type animals. We concluded that Prnp(0/0) mice show impairment of swimming capacity, perhaps reflecting impairment of muscular activity under more extreme exercise conditions. In spite of the mitochondrial abnormalities reported in Prnp(0/0) mice, our observation seems not to be related to MR. Our results indicate that further investigations should be conducted in order to improve our knowledge about the function of PrP(c) in muscle physiology and its possible role in several different neuromuscular pathologies.

Exploring the early steps of amyloid peptide aggregation by computers

The assembly of normally soluble proteins into amyloid fibrils is a hallmark of neurodegenerative diseases. Because protein aggregation is very complex, involving a variety of oligomeric metastable intermediates, the detailed aggregation paths and structural characterization of the intermediates remain to be determined. Yet, there is strong evidence that these oligomers, which form early in the process of fibrillogenesis, are cytotoxic. In this paper, we review our current understanding of the underlying factors that promote the aggregation of peptides into amyloid fibrils. We focus here on the structural and dynamic aspects of the aggregation as observed in state-of-the-art computer simulations of amyloid-forming peptides with an emphasis on the activation-relaxation technique.

Elongation of Ordered Peptide Aggregate of an Amyloidogenic Hexapeptide NFGAIL Observed in Molecular Dynamics Simulations with Explicit Solvent

The mechanisms by which amyloidogenic peptides and proteins form soluble toxic oligomers remain elusive. We have studied the formation of partially ordered tetramers and well-ordered octamers of an amyloidogenic hexapeptide NFGAIL (residues 22-27 of the human islet amyloid polypeptide) in our previous work. Continuing the effort, we here probe the beta-sheet elongation process by a combined total of 2.0 micros molecular dynamics simulations with explicit solvent. In a set of 10 simulations with the peptides restrained to the extended conformation, we observed that the main growth mode was elongation along the beta-sheet hydrogen bonds through primarily a two-stage process. Driven by hydrophobic forces, the peptides initially attached to the surface of the ordered oligomer, moved quickly to the beta-sheet edges, and formed stable beta-sheet hydrogen bonds. Addition of peptides to the existing oligomer notably improved the order of the peptide aggregate in which labile outer layer beta-sheets were stabilized, which provides good templates for further elongation. These simulations suggested that elongation along the beta-sheet hydrogen bonds occurs at the intermediate stage when low-weight oligomers start to form. We did not observe significant preference toward either parallel or antiparallel beta-sheets at the elongation stage for this peptide. In another set of 10 unrestrained simulations, the dominant growth mode was disordered aggregation. Taken together, these results offered a glimpse at the molecular events leading to the formation of ordered and disordered low-weight oligomers.

A toy model for predicting the rate of amyloid formation from unfolded protein

We develop a toy model for predicting the rate of amyloid formation from an unfolded polypeptide. The model assumes irreversible amyloid growth, employs a collision encounter scheme and uses a Gaussian chain approximation to describe the polypeptide sequence. A principal feature of the model is its dependence on a number of key sequence residues whose correct placement, geometric arrangement and orientation in relation to their interacting partners define the success, or otherwise, of the amyloid formation reaction. Although not realistic at the molecular level, the model captures some essential features of the system and is therefore useful from a heuristic standpoint. For the case of amyloid formation from an unstructured state, the model suggests that the major determinants of the rate of fibril formation are the length of the sequence separating the critical amino acids promoting amyloid formation and the positional placement of the critical residues within the sequence. Our findings suggest also that the sequence distance between the key interacting amino acid residues may play a role in defining the maximum width of a fibril and that the addition of non-interacting segments of long structure-less polypeptide chain to an amyloidogenic peptide may act to inhibit fibril formation. We discuss these findings with reference to the placement of critical sequence residues within the polypeptide chain, the design of polypeptides with lower amyloid formation propensities and the development of aggregation inhibitors as potential therapeutics for protein depositional disorders.

Protein-folding landscapes in multichain systems

Computational studies of proteins have significantly improved our understanding of protein folding. These studies are normally carried out by using chains in isolation. However, in many systems of practical interest, proteins fold in the presence of other molecules. To obtain insight into folding in such situations, we compare the thermodynamics of folding for a Miyazawa-Jernigan model 64-mer in isolation to results obtained in the presence of additional chains. The melting temperature falls as the chain concentration increases. In multichain systems, free-energy landscapes for folding show an increased preference for misfolded states. Misfolding is accompanied by an increase in interprotein interactions; however, near the folding temperature, the transition from folded chains to misfolded and associated chains is entropically driven. A majority of the most probable interprotein contacts are also native contacts, suggesting that native topology plays a role in early stages of aggregation.

Coarse-grained strategy for modeling protein stability in concentrated solutions

We present a coarse-grained approach for modeling the thermodynamic stability of single-domain globular proteins in concentrated aqueous solutions. Our treatment derives effective protein-protein interactions from basic structural and energetic characteristics of the native and denatured states. These characteristics, along with the intrinsic (i.e., infinite dilution) thermodynamics of folding, are calculated from elementary sequence information using a heteropolymer collapse theory. We integrate this information into Reactive Canonical Monte Carlo simulations to investigate the connections between protein sequence hydrophobicity, protein-protein interactions, protein concentration, and the thermodynamic stability of the native state. The model predicts that sequence hydrophobicity can affect how protein concentration impacts native-state stability in solution. In particular, low hydrophobicity proteins are primarily stabilized by increases in protein concentration, whereas high hydrophobicity proteins exhibit richer nonmonotonic behavior. These trends appear qualitatively consistent with the available experimental data. Although factors such as pH, salt concentration, and protein charge are also important for protein stability, our analysis suggests that some of the nontrivial experimental trends may be driven by a competition between destabilizing hydrophobic protein-protein attractions and entropic crowding effects.

Molecular dynamics and protein function

A fundamental appreciation for how biological macromolecules work requires knowledge of structure and dynamics. Molecular dynamics simulations provide powerful tools for the exploration of the conformational energy landscape accessible to these molecules, and the rapid increase in computational power coupled with improvements in methodology makes this an exciting time for the application of simulation to structural biology. In this Perspective we survey two areas, protein folding and enzymatic catalysis, in which simulations have contributed to a general understanding of mechanism. We also describe results for the F(1) ATPase molecular motor and the Src family of signaling proteins as examples of applications of simulations to specific biological systems.

The role of Phe in the formation of well-ordered oligomers of amyloidogenic hexapeptide (NFGAIL) observed in molecular dynamics simulations with explicit solvent

We observed fast aggregation of partially ordered oligomers in an earlier simulation study of an amyloidogenic hexapeptide NFGAIL. In this work, the nucleation of highly ordered oligomers was further investigated by a combined total of 960 ns molecular dynamics simulations with explicit solvent on NFGAIL and its nonamyloidogenic mutant NAGAIL. In these simulations, four dimer subunits that each was constrained by harmonic forces as a two-strand beta-sheet were used to enhance the rate of formation. It was found that a critical role played by the aromatic residue Phe was to direct the stacking of beta-sheets to form ordered multilayer aggregates. We also found that many molecular arrangements of the peptide satisfied the "cross-beta-structure", a hallmark of amyloid fibrils. The tendency for the peptide to form either parallel or antiparallel beta-sheet was comparable, as was the tendency for the beta-sheets to stack either in parallel or antiparallel orientation. Overall, approximately 85% of the native hexapeptide formed octamers. The fact that only 8% of the octamers were well-ordered species suggests that the dissociation of the disordered oligomers be the rate-limiting step in the formation of highly ordered oligomers. Among the well-ordered subunit pairs, about half was formed by the beta-sheet extension along the main-chain hydrogen-bond direction, whereas the other half was formed by the beta-sheet stacking. Hence, a delicate balance between intersheet and intrasheet interactions appeared to be crucial in the formation of a highly ordered nucleus of amyloid fibrils. The disordered oligomers were mainly stabilized by nonspecific hydrophobic interactions, whereas the well-ordered oligomers were further stabilized by cross-strand hydrogen bonds and favorable side-chain stacking.

Lattice models of peptide aggregation: Evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.

Kinetics of fibril formation by polyalanine peptides

Ordered beta-sheet complexes, termed amyloid fibrils, are the underlying structural components of the intra- and extracellular fibrillar protein deposits that are associated with a variety of human diseases, including Alzheimer's, Parkinson's, and the prion diseases. In this work, we investigated the kinetics of fibril formation using our newly developed off-lattice intermediate resolution model, PRIME. The model is simple enough to allow the treatment of large multichain systems while maintaining a fairly realistic description of protein dynamics without built-in bias toward any conformation when used in conjunction with constant temperature discontinuous molecular dynamics, a fast alternative to conventional molecular dynamics. Simulations were performed on systems containing 48-96 model Ac-KA14K-NH2 peptides. We found that fibril formation for polyalanines incorporate features that are characteristic of three models, the templated assembly, nucleated polymerization, and nucleated conformational conversion models, but that none of them gave a completely satisfactory description of the simulation kinetics. Fibril formation was nucleation-dependent, occurring after a lag time that decreased with increasing peptide concentration and increased with increasing temperature. Fibril formation appeared to be a conformational conversion process in which small amorphous aggregates --> beta-sheets --> ordered nucleus --> subsequent rapid growth of a small stable fibril or protofilament. Fibril growth in our simulations involved both beta-sheet elongation, in which the fibril grew by adding individual peptides to the end of each beta-sheet, and lateral addition, in which the fibril grew by adding already formed beta-sheets to its side. The initial rate of fibril formation increased with increasing concentration and decreased with increasing temperature.

Phase diagrams describing fibrillization by polyalanine peptides

Amyloid fibrils are the structural components underlying the intra- and extracellular protein deposits that are associated with a variety of human diseases, including Alzheimer's, Parkinson's, and the prion diseases. In this work, we examine the thermodynamics of fibril formation using our newly-developed off-lattice intermediate-resolution protein model, PRIME. The model is simple enough to allow the treatment of large multichain systems while maintaining a fairly realistic description of protein dynamics when used in conjunction with constant-temperature discontinuous molecular dynamics, a fast alternative to conventional molecular dynamics. We conduct equilibrium simulations on systems containing 96 Ac-KA14K-NH2 peptides over a wide range of temperatures and peptide concentrations using the replica-exchange method. Based on measured values of the heat capacity, radius of gyration, and percentage of peptides that form the various structures, a phase diagram in the temperature-concentration plane is constructed delineating the regions where each structure is stable. There are four distinct single-phase regions: alpha-helices, fibrils, nonfibrillar beta-sheets, and random coils; and four two-phase regions: random coils/nonfibrillar beta-sheets, random coils/fibrils, fibrils/nonfibrillar beta-sheets, and alpha-helices/nonfibrillar beta-sheets. The alpha-helical region is at low temperature and low concentration. The nonfibrillar beta-sheet region is at intermediate temperatures and low concentrations and expands to higher temperatures as concentration is increased. The fibril region occurs at intermediate temperatures and intermediate concentrations and expands to lower as the peptide concentration is increased. The random-coil region is at high temperatures and all concentrations; this region shifts to higher temperatures as the concentration is increased.