Activation-relaxation Technique Research Articles

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.

Exploring energy landscapes of protein folding and aggregation

Human diseases, such as Alzheimer's and Creutzfeldt-Jakob's are associated with misfolding and aggregation of specific proteins into amyloid fibrils sharing a generic cross-beta structure. The self-assembly process is complex, but once a nucleus is formed, rapid fibril formation occurs. Insight into the structures of the oligomers during the lag phase, varying between hours and days, is very difficult experimentally because these species are transient, and numerically using all-atom molecular dynamics because the time scale explored is on the order of 10-100 ns. It is therefore important to develop simplified protein models and alternative methods to sample more efficiently the conformational space. In the past few years, we have developed the activation-relaxation technique (ART nouveau) coupled to the OPEP coarse-grained force field. This review reports the application of ART-OPEP on protein folding and aggregation.

Ab-initio simulations of self-diffusion mechanisms in semiconductors

We present an application of SIEST-A-RT that combines the activation relaxation technique, ART nouveau, and the local-basis ab-initio code SIESTA, to study self-defect migration pathways in semiconductors. SIESTA provides reliable descriptions of defect properties in semiconductors directly comparable to experiment as well as, once combined with ART nouveau, a detailed description of their possible migration mechanisms. We use this package to characterize the properties of vacancies in silicon and GaAs, such as relaxation geometries, formation energies at low and high temperature, diffusion mechanisms and migration barriers. We show here that diffusion in bulk semiconductors is a rich and complex phenomenon that depends not only on the geometry of the defect and the surrounding lattice but also on its charge.

Sampling small-scale and large-scale conformational changes in proteins and molecular complexes

Sampling of small-scale and large-scale motions is important in various computational tasks, such as protein-protein docking and ligand binding. Here, we report further development and applications of the activation-relaxation technique for internal coordinate space trajectories (ARTIST). This method generates conformational moves of any complexity and size by identifying and crossing well-defined saddle points connecting energy minima. Simulations on two all-atom proteins and three protein complexes containing between 70 and 300 amino acids indicate that ARTIST opens the door to the full treatment of all degrees of freedom in dense systems such as protein-protein complexes.

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.

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.

Charge-dependent migration pathways for the Ga vacancy inGaAs

Using a combination of the local-basis ab initio program SIESTA and the activation-relaxation technique we study the diffusion mechanisms of the gallium vacancy in $\mathrm{GaAs}$. Vacancies are found to diffuse to the second neighbor using two different mechanisms, as well as to the first and fourth neighbors following various mechanisms. We find that the height of the energy barrier is sensitive to the Fermi level and generally increases with the charge state. Migration pathways themselves can be strongly charge dependent and may appear or disappear as a function of the charge state. These differences in transition state and migration barrier are explained by the charge transfer that takes place during the vacancy migration.

Aggregating the amyloid Aβ11–25 peptide into a four‐stranded β‐sheet structure

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

The conformations of the amyloid-β (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.

Exploiting memory in event-based simulations

Few simulation methods have succeeded in sampling efficiently the phase space of complex systems with a dynamics dominated by activated events. In order to address this limitation, we have recently introduced an activated algorithm based on a mixture of the activation-relaxation technique and molecular dynamics (the properly obeying probability activation relaxation technique, POP-ART). We show here that the basic implementation of POP-ART is only as fast as MD in sampling the phase space of a complex material, amorphous silicon at 600K. However, as the activation moves are locally defined, it is possible to use a number of tricks that can increase significantly sampling efficiency of POP-ART. We consider an approach, the memory kernel, based on avoiding recently encountered moves and show using a simple model that this introduces very little bias while ensuring a significant gain over standard Monte Carlo in sampling the phase space of this model. Incorporating the memory kernel into POP-ART improves considerably its efficiency in sampling the phase space of amorphous silicon as compared to standard POP-ART and molecular dynamics.

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.

Exploring the Early Steps of Amyloid Peptide Aggregation by Computers

AbstractFor Abstract see ChemInform Abstract in Full Text.

Activated sampling in complex materials at finite temperature: The properly obeying probability activation-relaxation technique

While the dynamics of many complex systems is dominated by activated events, there are very few simulation methods that take advantage of this fact. Most of these procedures are restricted to relatively simple systems or, as with the activation-relaxation technique (ART), sample the conformation space efficiently at the cost of a correct thermodynamical description. We present here an extension of ART, the properly obeying probability ART (POP-ART), that obeys detailed balance and samples correctly the thermodynamic ensemble. Testing POP-ART on two model systems, a vacancy and an interstitial in crystalline silicon, we show that this method recovers the proper thermodynamical weights associated with the various accessible states and is significantly faster than molecular dynamics in the simulations of a vacancy below 700 K.

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 β-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.

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.

Structural and dielectric properties of crystalline and amorphous ZrO 2

We first review earlier work in which we computed the first-principles structural, vibrational, and lattice dielectric properties of the cubic, tetragonal, and monoclinic phases of ZrO 2 and HfO 2. We then discuss two approaches to the construction of realistic models of amorphous ZrO 2: a “melt-and-quench” ab-initio molecular dynamics approach, and an “activation–relaxation technique”. The structural, vibrational, and dielectric properties of the resulting models are then analyzed in detail. The overall average dielectric constant is computed and found to be comparable to that of the monoclinic phase. These techniques show promise for future modeling of high-K dielectric ultrathin films and interfaces.

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 β-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.

Exploring the early steps of aggregation of amyloid-forming peptide KFFE

It has been shown recently that even a tetrapeptide can form amyloid fibrils sharing all thecharacteristics of amyloid fibrils built from large proteins. Recent experimental studies alsosuggest that the toxicity observed in several neurodegenerative diseases, such asAlzheimer’s disease and Creutzfeldt–Jakob disease, is not only related to themature fibrils themselves, but also to the soluble oligomers formed early in theprocess of fibrillogenesis. This raises the interest in studying the early steps of theaggregation process. Although fibril formation follows the nucleation–condensationprocess, characterized by the presence of lag phase, the exact pathways remain to bedetermined. In this study, we used the activation–relaxation technique and ageneric energy model to explore the process of self-assembly and the structures ofthe resulting aggregates of eight KFFE peptides. Our simulations show, startingfrom different states with a preformed antiparallel dimer, that eight chains canself-assemble to adopt, with various orientations, four possible distant oligomericwell-aligned structures of similar energy. Two of these structures show a double-layerβ-sheet organization, in agreement with the structure of amyloid fibrils as observed by x-raydiffraction; another two are mixtures of dimers and trimers. Our results also suggest thatoctamers are likely to be below the critical size for nucleation of amyloid fibrils for smallpeptides.

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.