Generating ensemble averages for small proteins from extended conformations by Monte Carlo simulations

Computer Simulations Aimed at Exploring Protein Aggregation and Dissociation

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

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

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

Tau R3-R4 Domain Dimer of the Wild Type and Phosphorylated Ser356 Sequences. I. In Solution by Atomistic Simulations

In Alzheimer's disease, neurofibrillary lesions correlate with cognitive deficits and consist of inclusions of tau protein with cross-β structure. A stable dimeric form of soluble tau has been evidenced in the cells, but its high-resolution structure is missing in solution. We know, however, that cryo-electron microscopy (c-EM) of full-length tau in the brain of an individual with AD displays a core of eight β-sheets with a C-shaped architecture spanning the R3-R4 repeat domain, while the rest of the protein is very flexible. To address the conformational ensemble of the dimer, we performed atomistic replica exchange molecular dynamics simulations on the tau R3-R4 domain starting from the c-EM configuration. We find that the wild type tau R3-R4 dimer explores elongated, U-shaped, V-shaped, and globular forms rather than the C-shape. Phosphorylation of Ser356, pSer356, is known to block the interaction between the tau protein and the amyloid-β42 peptide. Standard molecular dynamics simulations of this phosphorylated sequence for a total of 5 μs compared to its wild type counterpart show a modulation of the population of β-helices and accessible topologies and a decrease of intermediates near the fibril-like conformers.

Aggregation of disease-related peptides

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

Amyloid-β(29-42) Dimeric Conformations in Membranes Rich in Omega-3 and Omega-6 Polyunsaturated Fatty Acids

The omega-3 and omega-6 polyunsaturated fatty acids are two important components of cell membranes in human brains. When incorporated into phospholipids, omega-3 slows the progression of Alzheimer's disease (AD), whereas omega-6 is linked to increased risk of AD. Little is known on the amyloid-β (Aβ) conformations in membranes rich in omega-3 and omega-6 phospholipids. Herein, the structural properties of the Aβ_29-42 dimer embedded in both fatty acid membranes were comparatively studied to a 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine (POPC) bilayer using all-atom molecular dynamics (MD) simulations. Starting from α-helix, both omega-6 and omega-3 membranes promote new orientations and conformations of the dimer, in agreement with the observed dependence of Aβ production upon addition of these two fatty acids. This conformational result is corroborated by atomistic MD simulations of the dimer of the 99 amino acid C-terminal fragment of amyloid precursor protein spanning the residues 15-55. Starting from β-sheet, omega-6 membrane promotes helical and disordered structures of Aβ_29-42 dimer, whereas omega-3 membrane preserves the β-sheet structures differing however from those observed in POPC. Remarkably, the mixture of the two fatty acids and POPC depicts another conformational ensemble of the Aβ_29-42 dimer. This finding demonstrates that variation in the abundance of the molecular phospholipids, which changes with age, modulates membrane-embedded Aβ oligomerization.

Multi-scale simulations of biological systems using the OPEP coarse-grained model

Biomolecules are complex machines that are optimized by evolution to properly fulfill or contribute to a variety of biochemical tasks in the cellular environment. Computer simulations based on quantum mechanics and atomistic force fields have been proven to be a powerful microscope for obtaining valuable insights into many biological, physical, and chemical processes. Many interesting phenomena involve, however, a time scale and a number of degrees of freedom, notably if crowding is considered, that cannot be explored at an atomistic resolution. To bridge the gap between reality and simulation, many different advanced computational techniques and coarse-grained (CG) models have been developed. Here, we report some applications of the CG OPEP protein model to amyloid fibril formation, the response of catch-bond proteins to two types of fluid flow, and interactive simulations to fold peptides with well-defined 3D structures or with intrinsic disorder.

The OPEP protein model: from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems

The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows the study of single protein properties, DNA-RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then present the current limitations and a perspective on the ongoing developments.

Importance of the ion-pair interactions in the OPEP coarse-grained force field: parametrization and validation

We have derived new effective interactions that improve the description of ion-pairs in the OPEP coarse-grained force field without introducing explicit electrostatic terms. The iterative Boltzmann inversion method was used to extract these potentials from all atom simulations by targeting the radial distribution function of the distance between the center of mass of the side-chains. The new potentials have been tested on several systems that differ in structural properties, thermodynamic stabilities and number of ion-pairs. Our modeling, by refining the packing of the charged amino-acids, impacts the stability of secondary structure motifs and the population of intermediate states during temperature folding/unfolding; it also improves the aggregation propensity of peptides. The new version of the OPEP force field has the potentiality to describe more realistically a large spectrum of situations where salt-bridges are key interactions.

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

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

Coarse-grained models for protein folding and aggregation

Coarse-grained models for protein folding and aggregation are used to explore large dimension scales and timescales that are inaccessible to all-atom models in explicit aqueous solution. Combined with enhanced configuration search methods, these simplified models with various levels of granularity offer the possibility to determine equilibrium structures, compare folding kinetics and thermodynamics with experiments for single proteins and understand the dynamic assembly of amyloid proteins leading to neurodegenerative diseases. I shall describe recent progress in developing such models, and discuss their potentials and limitations in probing the folding and misfolding of proteins with computer simulations.

Kinetics of amyloid aggregation: a study of the GNNQQNY prion sequence

The small amyloid-forming GNNQQNY fragment of the prion sequence has been the subject of extensive experimental and numerical studies over the last few years. Using unbiased molecular dynamics with the OPEP coarse-grained potential, we focus here on the onset of aggregation in a 20-mer system. With a total of 16.9 of simulations at 280 K and 300 K, we show that the GNNQQNY aggregation follows the classical nucleation theory (CNT) in that the number of monomers in the aggregate is a very reliable descriptor of aggregation. We find that the critical nucleus size in this finite-size system is between 4 and 5 monomers at 280 K and 5 and 6 at 300 K, in overall agreement with experiment. The kinetics of growth cannot be fully accounted for by the CNT, however. For example, we observe considerable rearrangements after the nucleus is formed, as the system attempts to optimize its organization. We also clearly identify two large families of structures that are selected at the onset of aggregation demonstrating the presence of well-defined polymorphism, a signature of amyloid growth, already in the 20-mer aggregate.

Protein aggregation plays an important pathological role in numerous neurodegenerative diseases such as Alzheimer's, Parkinson's, Creutzfeldt-Jakob, the Prion disease and diabetes mellitus. In most cases, misfolded proteins are involved and aggregate irreversibly to form highly ordered insoluble macrostructures, called amyloid fibrils, which deposit in the brain. Studies have revealed that all proteins are capable of forming amyloid fibrils that all share common structural features and therefore aggregation mechanisms. The toxicity of amyloid aggregates is however not attributed to the fibrils themselves but rather to smaller more disordered aggregates, oligomers, forming parallel to or prior to fibrils. Understanding the assembly process of these amyloid oligomers is key to understanding their toxicity mechanism in order to devise a possible treatment strategy targeting these toxic aggregates. Our approach here is to computationally study the aggregation dynamics of a 20-mer of an amyloid peptide GNNQQNY from a prion protein. Our findings suggest that the assembly is a spontaneous process that can be described as a complex nucleation and growth mechanism and which can lead to two classes of morphologies for the aggregates, one of which resembles a protofibril-like structure. Such numerical studies are crucial to understanding the details of fast biological processes and complement well experimental studies.

Flexibility and binding affinity in protein-ligand, protein-protein and multi-component protein interactions: limitations of current computational approaches

The recognition process between a protein and a partner represents a significant theoretical challenge. In silico structure-based drug design carried out with nothing more than the three-dimensional structure of the protein has led to the introduction of many compounds into clinical trials and numerous drug approvals. Central to guiding the discovery process is to recognize active among non-active compounds. While large-scale computer simulations of compounds taken from a library (virtual screening) or designed de novo are highly desirable in the post-genomic area, many technical problems remain to be adequately addressed. This article presents an overview and discusses the limits of current computational methods for predicting the correct binding pose and accurate binding affinity. It also presents the performances of the most popular algorithms for exploring binary and multi-body protein interactions.

A coarse-grained protein force field for folding and structure prediction

We have revisited the protein coarse-grained optimized potential for efficient structure prediction (OPEP). The training and validation sets consist of 13 and 16 protein targets. Because optimization depends on details of how the ensemble of decoys is sampled, trial conformations are generated by molecular dynamics, threading, greedy, and Monte Carlo simulations, or taken from publicly available databases. The OPEP parameters are varied by a genetic algorithm using a scoring function which requires that the native structure has the lowest energy, and the native-like structures have energy higher than the native structure but lower than the remote conformations. Overall, we find that OPEP correctly identifies 24 native or native-like states for 29 targets and has very similar capability to the all-atom discrete optimized protein energy model (DOPE), found recently to outperform five currently used energy models.

Replica exchange molecular dynamics simulations of coarse-grained proteins in implicit solvent

Current approaches aimed at determining the free energy surface of all-atom medium-size proteins in explicit solvent are slow and are not sufficient to converge to equilibrium properties. To ensure a proper sampling of the configurational space, it is preferable to use reduced representations such as implicit solvent and/or coarse-grained protein models, which are much lighter computationally. Each model must be verified, however, to ensure that it can recover experimental structures and thermodynamics. Here we test the coarse-grained implicit solvent OPEP model with replica exchange molecular dynamics (REMD) on six peptides ranging in length from 10 to 28 residues: two alanine-based peptides, the second beta-hairpin from protein G, the Trp-cage and zinc-finger motif, and a dimer of a coiled coil peptide. We show that REMD-OPEP recovers the proper thermodynamics of the systems studied, with accurate structural description of the beta-hairpin and Trp-cage peptides (within 1-2 A from experiments). The light computational burden of REMD-OPEP, which enables us to generate many hundred nanoseconds at each temperature and fully assess convergence to equilibrium ensemble, opens the door to the determination of the free energy surface of larger proteins and assemblies.

The fast-folding HP35 double mutant has a substantially reduced primary folding free energy barrier

The LYS24/29NLE double mutant of villin headpiece subdomain (HP35) is the fastest folding protein known so far with a folding time constant of 0.6 micros. In this work, the folding mechanism of the mutant has been investigated by both conventional and replica exchange molecular dynamics (CMD and REMD) simulations with AMBER FF03 force field and a generalized-Born solvation model. Direct comparison to the ab initio folding of the wild type HP35 enabled a close examination on the mutational effect on the folding process. The mutant folded to the native state, as demonstrated by the 0.50 A C(alpha)-root mean square deviation (RMSD) sampled in both CMD and REMD simulations and the high population of the folded conformation compared with the denatured conformations. Consistent with experiments, the significantly reduced primary folding free energy barrier makes the mutant closer to a downhill folder than the wild type HP35 that directly leads to the faster transition and higher melting temperature. However, unlike the proposed downhill folding which envisages a smooth shift between unfolded and folded states without transition barrier, we observed a well-defined folding transition that was consistent with experiments. Further examination of the secondary structures revealed that the two mutated residues have higher intrinsic helical preference that facilitated the formation of both helix III and the intermediate state which contains the folded segment helix II/III. Other factors contributing to the faster folding include the more favorable electrostatic interactions in the transition state with the removal of the charged NH(3)(+) groups from LYS. In addition, both transition state ensemble and denatured state ensemble are shifted in the mutant.

Energy landscapes of the monomer and dimer of the Alzheimer's peptide Abeta(1-28)

The cytotoxicity of Alzheimer's disease has been linked to the self-assembly of the 4042 amino acid of the amyloid-beta (Abeta) peptide into oligomers. To understand the assembly process, it is important to characterize the very first steps of aggregation at an atomic level of detail. Here, we focus on the N-terminal fragment 1-28, known to form fibrils in vitro. Circular dichroism and NMR experiments indicate that the monomer of Abeta(1-28) is alpha-helical in a membranelike environment and random coil in aqueous solution. Using the activation-relaxation technique coupled with the OPEP coarse grained force field, we determine the structures of the monomer and of the dimer of Abeta(1-28). In agreement with experiments, we find that the monomer is predominantly random coil in character, but displays a non-negligible beta-strand probability in the N-terminal region. Dimerization impacts the structure of each chain and leads to an ensemble of intertwined conformations with little beta-strand content in the region Leu17-Ala21. All these structural characteristics are inconsistent with the amyloid fibril structure and indicate that the dimer has to undergo significant rearrangement en route to fibril formation.

The complex folding pathways of protein A suggest a multiple-funnelled energy landscape

Folding proteins into their native states requires the formation of both secondary and tertiary structures. Many questions remain, however, as to whether these form into a precise order, and various pictures have been proposed that place the emphasis on the first or the second level of structure in describing folding. One of the favorite test models for studying this question is the B domain of protein A, which has been characterized by numerous experiments and simulations. Using the activation-relaxation technique coupled with a generic energy model (optimized potential for efficient peptide structure prediction), we generate more than 50 folding trajectories for this 60-residue protein. While the folding pathways to the native state are fully consistent with the funnel-like description of the free energy landscape, we find a wide range of mechanisms in which secondary and tertiary structures form in various orders. Our nonbiased simulations also reveal the presence of a significant number of non-native beta and alpha conformations both on and off pathway, including the visit, for a non-negligible fraction of trajectories, of fully ordered structures resembling the native state of nonhomologous proteins.

Modeling amyloid fibril formation: a free-energy approach

Amyloid fibrils are structures consisting of many proteins with a well-defined conformation. The formation of these fibrils has been the subject of intense research, largely due to their connection to several diseases. We focus here on the computational studies and discuss these from a free-energy point of view. The fibrillogenic properties of many proteins can be predicted and understood by taking the relevant free energies into account in an appropriate way. This is because both the equilibrium and the kinetic properties of the protein system depend on its free-energy landscape. Advanced simulation techniques can be used to understand the relationship between the free-energy landscape of a protein and its three-dimensional structure and propensity to form amyloid fibrils. We give an overview of existing simulation techniques that operate at a molecular level of detail and that are capable of generating relevant free-energy values. The free energies obtained with these methods can be inserted into a statistical-mechanical or kinetic framework to predict mean fibril properties on length scales and time scales that are inaccessible by molecular-scale simulation methods.

The conformations of the amyloid-beta (21-30) fragment can be described by three families in solution

Alzheimer's disease has been linked to the self-assembly of the amyloid-beta protein of 40 and 42 residues. Although monomers are in equilibrium with higher-order species ranging from dimers to heptamers, structural knowledge of the monomeric amyloid-beta (Abeta) peptides is an important issue. Recent experimental data have shown that the fragment (21-30) is protease-resistant within full-length Abeta peptides and displays two structural families in solution. Because the details of the Abeta(21-30) structures found using distinct force fields and protocols differ at various degrees from those of the NMR structures, we revisit the conformational space of this peptide using the activation-relaxation technique (ART nouveau) coupled with a coarse-grained force field (OPEP v.3.0). We find that although Abeta(21-30) does not have a secondary structure, it dominantly populates three structural families, with a loop spanning residues Val24-Lys28. The first two families, which differ in the nature of the electrostatic interactions, satisfy the five interproton rotating frame nuclear Overhauser effect spectroscopy (ROESY) distances and superpose well onto the NMR structures. The third family, which cannot be seen by ROESY NMR experiments, displays a more open structure. This numeric study complements the experimental results by providing a much more detailed description of the dominant structures. Moreover, it provides further evidence of the capability of ART OPEP in providing a reliable conformational picture of peptides in solution.

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.

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.

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.

Molecular dynamics simulations of folding processes of a β-hairpin in an implicit solvent

Computer simulations of beta-hairpin folding are relatively difficult, especially those based on the explicit water model. This greatly limits the complete analysis and understanding of their folding mechanisms. In this paper, we use the generalized Born/solvent accessible implicit solvent model to simulate the folding processes of a nine-residue beta-hairpin. We find that the beta-hairpin can fold into its native structure very easily, even using the traditional molecular dynamics method. This allows us to extract 21 complete folding events and investigate the folding process sufficiently. Our results show that there exist four most stable states on the free energy landscape of the short peptide, one native state and three intermediates. We find that two of the non-native stable states have almost the same potential energy as the native state but with lower entropy. This suggests that the native state can be stabilized entropically. Furthermore, we find that the folding processes of this peptide have common features: to fold into its native state, the peptide undergoes a continuous collapsing-extending-recollapsing process to adjust the positions of the side chains in order to form the native middle inter-strand hydrogen bonds. The formations of these bonds are the key step of the folding process. Once these bonds are formed, the peptide can fold into the native state quickly.

ARTIST: An activated method in internal coordinate space for sampling protein energy landscapes

We present the first applications of an activated method in internal coordinate space for sampling all-atom protein conformations, the activation-relaxation technique for internal coordinate space trajectories (ARTIST). This method differs from all previous internal coordinate-based studies aimed at folding or refining protein structures in that conformational changes result from identifying and crossing well-defined saddle points connecting energy minima. Our simulations of four model proteins containing between 4 and 47 amino acids indicate that this method is efficient for exploring conformational space in both sparsely and densely packed environments, and offers new perspectives for applications ranging from computer-aided drug design to supramolecular assembly.

Navigation and analysis of the energy landscape of small proteins using the activation–relaxation technique

The resolution of the protein folding problem has been tied to the development of a detailed understanding of the configurational energy or of the free energy landscape associated with these molecules. Using the activation-relaxation technique and a simplified energy model, we present here a detailed analysis of the energy landscape of 16-residue peptide that folds into a beta-hairpin. Our results support the concept of an energy landscape with an effective topology consistent with a scale-free network.

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.

Pathway complexity of Alzheimer's beta-amyloid Abeta16-22 peptide assembly

Recent studies suggest that both soluble oligomers and insoluble fibrils have toxic effects in cell cultures, raising the interest in determining the first steps of the assembly process. We have determined the aggregation mechanisms of Abeta(16-22) dimer using the activation-relaxation technique and an approximate free energy model. Consistent with the NMR solid-state analysis, the dimer is predicted to prefer an antiparallel beta sheet structure with the expected registry of intermolecular hydrogen bonds. The simulations, however, locate three other antiparallel minima with nonnative beta sheet registries and one parallel beta sheet structure, slightly destabilized with respect to the ground state. This result is significant because it can explain the observed dependency of beta sheet registry on pH conditions. We also find that assembly of Abeta(16-22) into dimers follows multiple routes, but alpha-helical intermediates are not obligatory. This indicates that destabilization of alpha-helical intermediates is unlikely to abolish oligomerization of Abeta peptides.

Complex folding pathways in a simple beta-hairpin

The determination of the folding mechanisms of proteins is critical to understand the topological change that can propagate Alzheimer and Creutzfeld-Jakobs diseases, among others. The computational community has paid considerable attention to this problem; however, the associated time scale, typically on the order of milliseconds or more, represents a formidable challenge. Ab initio protein folding from long molecular dynamics simulations or ensemble dynamics is not feasible with ordinary computing facilities and new techniques must be introduced. Here we present a detailed study of the folding of a 16-residue beta-hairpin, described by a generic energy model and using the activation-relaxation technique. From a total of 90 trajectories at 300 K, three folding pathways emerge. All involve a simultaneous optimization of the complete hydrophobic and hydrogen bonding interactions. The first two pathways follow closely those observed by previous theoretical studies (folding starting at the turn or by interactions between the termini). The third pathway, never observed by previous all-atom folding, unfolding, and equilibrium simulations, can be described as a reptation move of one strand of the beta-sheet with respect to the other. This reptation move indicates that non-native interactions can play a dominant role in the folding of secondary structures. Furthermore, such a mechanism mediated by non-native hydrogen bonds is not available for study by unfolding and Gō model simulations. The exact folding path followed by a given beta-hairpin is likely to be influenced by its sequence and the solvent conditions. Taken together, these results point to a more complex folding picture than expected for a simple beta-hairpin.

In silico assembly of Alzheimer's Abeta16-22 peptide into beta-sheets

Recent studies suggest that soluble oligomers of amyloid-forming peptides have toxic effects in cell cultures. In this study, the folding of three Alzheimer's A beta(16-22) peptides have been simulated with the activation-relaxation technique and a generic energy model. Starting from randomly chosen states, the predicted lowest energy structure superposes within 1 A rms deviation from its conformation within the fibrils. This antiparallel structure is found to be in equilibrium with several out-of-register antiparallel beta-sheets and mixed parallel-antiparallel beta-sheets, indicating that full structural order in the fibrils requires larger aggregates. Folding involves the formation of dimers followed by the addition of a monomer and proceeds through a generalized mechanism between disordered and native alignments of beta-strands.

Sampling the self-assembly pathways of KFFE hexamers

The formation of amyloid fibrils is often encountered in Alzheimer's disease, type II diabetes, and transmissible spongiform encephalopathies. In the last few years, however, mounting evidence has suggested that the soluble oligomers of amyloid-forming peptides are also cytotoxic agents. Understanding the early pathway steps of amyloid self-assembly at atomic detail might therefore be crucial for the development of specific inhibitors to prevent amyloidosis in humans. Using the activation-relaxation technique and a generic energy model, we study in detail the aggregation of a hexamer of KFFE peptide. Our simulations show that a monomer remains disordered, but that six monomers placed randomly in an open box self-associate to adopt, with various orientations, three possible distant low-energy structures. Two of these structures show a double-layer beta-sheet organization, in agreement with the structure of amyloid fibrils as observed by x-ray diffraction, whereas the third one consists of a barrel-like curved single-layer hexamer. Based on these results, we propose a bidirectional growth mode of amyloid fibril, involving alternate lateral and longitudinal growths.

Polypeptide Folding Using Monte Carlo Sampling, Concerted Rotation, and Continuum Solvation

An efficient concerted rotation algorithm for use in Monte Carlo statistical mechanics simulations is applied to fold three polypeptides, U(1-17)T9D, alpha(1), and trpzip2, which exhibit native beta-hairpin and alpha-helix folds. The method includes flexible bond and dihedral angles, and a Gaussian bias is applied with driver bond and dihedral angles to optimize the sampling efficiency. Solvation in water is implemented with the generalized Born (GBSA) model. The computed lowest-energy manifolds for the folded structures of the two beta-hairpins agree closely with the corresponding NMR structures. In the case of the alpha(1) peptide, the folded alpha-helical state, which is observed as oligomers in concentrated solution and crystals, is not stable in isolation. The computed preference for random coil structures is in agreement with NMR experiments at low concentration. The fact that native states can be located on high dimensional energy surfaces starting from extended conformations shows that the present methodology samples all relevant parts of the conformational space. The OPLS-AA force field with the GBSA solvent model was also found to perform well in leading to clear energetic separation of the correctly folded structures from misfolded structures for the two peptides that form beta-turns.

Sampling activated mechanisms in proteins with the activation-relaxation technique

The activated dynamics of proteins occur on time scales of milliseconds and longer. Standard all-atom molecular dynamics simulations are limited to much shorter times, of the order of tens of nanoseconds. Therefore, many activated mechanisms that are crucial for long-time dynamics will not be observed in such molecular dynamics simulation; different methods are required. Here, we describe in detail the activation-relaxation technique (ART) that generates directly activated mechanisms. The method is defined in the configurational energy landscape and defines moves in a two step fashion: (a) a configuration is first brought from a local minimum to a nearby first-order saddle point (the activation); and (b) the configuration is relaxed to a new metastable state (the relaxation). The method has already been applied to a wide range of problems in condensed matter, including metallic glasses, amorphous semiconductors and silica glass. We review the algorithm in detail, discuss some previously published results and present simulations of activated mechanisms for a two-helix bundle protein using an all-atom energy function.

Computer simulations aimed at structure prediction of supersecondary motifs in proteins

It is well established that protein structures are more conserved than protein sequences. One-third of all known protein structures can be classified into ten protein folds, which themselves are composed mainly of alpha-helical hairpin, beta hairpin, and betaalphabeta supersecondary structural elements. In this study, we explore the ability of a recent Monte Carlo-based procedure to generate the 3D structures of eight polypeptides that correspond to units of supersecondary structure and three-stranded antiparallel beta sheet. Starting from extended or misfolded compact conformations, all Monte Carlo simulations show significant success in predicting the native topology using a simplified chain representation and an energy model optimized on other structures. Preliminary results on model peptides from nucleotide binding proteins suggest that this simple protein folding model can help clarify the relation between sequence and topology.

Evidence that the 127-164 region of prion proteins has two equi-energetic conformations with beta or alpha features

Prion proteins cause neurodegenerative illnesses in humans and animals. The diseases are associated with a topological change from a predominantly alpha (PrP(C)) to beta-sheet (PrP(Sc)) structure. Many studies have focused on the minimum sequence requirements and key events for developing or transmitting disease. Here, we report on the application of molecular modeling studies to predict the lowest-energy conformations for five fragments in solution at pH 7. We show that PrP(143-158) adopts a helix, the model PrP(106-126), PrP(142-167), and PrP(143-178) peptides have a clear preference for a variety of beta-sheet structures, whereas PrP(127-164) has two iso-energetic conformations with all beta or alphabeta native-like structures. Such a finding for PrP(127-164), which explains a large body of experimental data, including the location of all mutations causing prion diseases, may have important implications for triggering or propagating the topological change.