Study of the Villin headpiece folding dynamics by combining coarse-grained Monte Carlo evolution and all-atom molecular dynamics

The folding mechanism of the Villin headpiece (HP36) is studied by means of a novel approach which entails an initial coarse-grained Monte Carlo (MC) scheme followed by all-atom molecular dynamics (MD) simulations in explicit solvent. The MC evolution occurs in a simplified free-energy landscape and allows an efficient selection of marginally-compact structures which are taken as viable initial conformations for the MD. The coarse-grained MC structural representation is connected to the one with atomic resolution through a "fine-graining" reconstruction algorithm. This two-stage strategy is used to select and follow the dynamics of seven different unrelated conformations of HP36. In a notable case the MD trajectory rapidly evolves towards the folded state, yielding a typical root-mean-square deviation (RMSD) of the core region of only 2.4 A from the closest NMR model (the typical RMSD over the whole structure being 4.0 A). The analysis of the various MC-MD trajectories provides valuable insight into the details of the folding and mis-folding mechanisms and particularly about the delicate influence of local and nonlocal interactions in steering the folding process.     

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

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

Backbone dynamics, fast folding, and secondary structure formation in helical proteins and peptides

We discuss the construction of a simple, off-lattice model protein with a comparatively detailed representation of the protein backbone, and use it to address some general aspects of the folding kinetics of a small helical protein and two peptide fragments. The model makes use of an associative memory hamiltonian to smoothly interpolate between the limits of a native contact only, or Go, potential and a statistical pair potential derived from a database of known structures. We have observed qualitatively different behavior in these two limits. In the Go limit, we see apparently barrier-less folding. As we increase the roughness of the model energy landscape, we can observe the emergence of the characteristic activated temperature dependence previously seen in lattice studies and analytical theories. We are also able to study the dependence of the folding kinetics on local interactions such as hydrogen bonds, and we discuss the implications of these results for the formation of secondary structure at intermediate stages of the folding reaction.     

Principal component analysis for protein folding dynamics

Protein folding is considered here by studying the dynamics of the folding of the triple β-strand WW domain from the Formin-binding protein 28. Starting from the unfolded state and ending either in the native or nonnative conformational states, trajectories are generated with the coarse-grained united residue (UNRES) force field. The effectiveness of principal components analysis (PCA), an already established mathematical technique for finding global, correlated motions in atomic simulations of proteins, is evaluated here for coarse-grained trajectories. The problems related to PCA and their solutions are discussed. The folding and nonfolding of proteins are examined with free-energy landscapes. Detailed analyses of many folding and nonfolding trajectories at different temperatures show that PCA is very efficient for characterizing the general folding and nonfolding features of proteins. It is shown that the first principal component captures and describes in detail the dynamics of a system. Anomalous diffusion in the folding/nonfolding dynamics is examined by the mean-square displacement (MSD) and the fractional diffusion and fractional kinetic equations. The collisionless (or ballistic) behavior of a polypeptide undergoing Brownian motion along the first few principal components is accounted for.     

Theoretical investigation of the photoinitiated folding of HP-36

A computational model was developed to examine the phototriggered folding of a caged protein, a protein modified with an organic photolabile cross-linker. Molecular dynamics simulations of the modified 36-residue fragment of subdomain B of chicken villin head piece with a photolabile linker were performed, starting from both the caged and the uncaged structures. Construction of a free-energy landscape, based on principal components as well as on radius of gyration versus root-mean-square deviation, and circular dichroism calculations were employed to characterize folding behavior and structures. The folded structures observed in the molecular dynamics trajectories were found to be similar to that of the wild-type protein, in agreement with the published experimental results. The free-energy landscapes of the modified and wild-type proteins have similar topology, suggesting common thermodynamic/kinetic behavior. The existence of small differences in the free-energy surface of the modified protein from that of the native protein, however, indicates subtle differences in the folding behavior.     

Putative Active States of a Prototypic G-Protein-Coupled Receptor from Biased Molecular Dynamics

A major current focus of structural work on G-protein-coupled receptors (GPCRs) pertains to the investigation of their active states. However, for virtually all GPCRs, active agonist-bound intermediate states have been difficult to characterize experimentally owing to their higher conformational flexibility, and thus intrinsic instability, as compared to inactive inverse agonist-bound states. In this work, we explored possible activation pathways of the prototypic GPCR bovine rhodopsin by means of biased molecular dynamics simulations. Specifically, we used an explicit atomistic representation of the receptor and its environment, and sampled the conformational transition from the crystal structure of a photoactivated deprotonated state of rhodopsin to the low pH crystal structure of opsin in the presence of 11-trans-retinal, using adiabatic biased molecular dynamics simulations. We then reconstructed the system free-energy landscape along the predetermined transition trajectories using a path collective variable approach based on metadynamics. Our results suggest that the two experimental endpoints of rhodopsin/opsin are connected by at least two different pathways, and that the conformational transition is populated by at least four metastable states of the receptor, characterized by a different amplitude of the outward movement of transmembrane helix 6.     

Molecular dynamics simulation of amyloid beta dimer formation

Recent experiments with amyloid beta (Abeta) peptide indicate that formation of toxic oligomers may be an important contribution to the onset of Alzheimer's disease. The toxicity of Abeta oligomers depends on their structure, which is governed by assembly dynamics. Due to limitations of current experimental techniques, a detailed knowledge of oligomer structure at the atomic level is missing. We introduce a molecular dynamics approach to study Abeta dimer formation. 1), We use discrete molecular dynamics simulations of a coarse-grained model to identify a variety of dimer conformations; and 2), we employ all-atom molecular mechanics simulations to estimate thermodynamic stability of all dimer conformations. Our simulations of a coarse-grained Abeta peptide model predicts 10 different planar beta-strand dimer conformations. We then estimate the free energies of all dimer conformations in all-atom molecular mechanics simulations with explicit water. We compare the free energies of Abeta(1-42) and Abeta(1-40) dimers. We find that 1), dimer conformations have higher free energies compared to their corresponding monomeric states; and 2), the free-energy difference between the Abeta(1-42) and the corresponding Abeta(1-40) dimer conformation is not significant. Our results suggest that Abeta oligomerization is not accompanied by the formation of thermodynamically stable planar beta-strand dimers.     

Enhanced analysis of landscape structure: Inclusion of transition zones and small-scale landscape elements

Landscape diversity is an essential component of biodiversity because it determines the diversity of habitats and species. It is necessary to adopt an adaptive and realizable landscape structure monitoring model for ecosystem management. However, the existing methods of landscape structure analysis often do not consider the transitions between different types of patch, which are dynamic and play several functional roles in landscape structure. Another component of information that has often been ignored is “small-scale landscape elements” inside patches, which leads to within-patch heterogeneity being underestimated. This paper presents a method for solving these problems by regular landscape monitoring using RapidEye remote sensing data. We incorporate the third altitude dimension in landscape structure analysis, especially for detecting certain small-scale landscape structures such as groves, tree rows, and transitions at forest boundaries. For these detailed structures a number of landscape metrics are computed under a three-dimensional perspective. The results indicate that a more realistic and more precise representation of landscape structure is obtained on the basis of the detailed spatial scale and the true surface geometries of patches. Taking transitions into account helps smooth “edge effects” between patches and leads to more realistic quantification of fragmentation.     

Zipping and Unzipping of Adenylate Kinase: Atomistic Insights into the Ensemble of Open ↔ Closed Transitions

Adenylate kinase (AdK), a phosphotransferase enzyme, plays an important role in cellular energy homeostasis. It undergoes a large conformational change between an open and a closed state, even in the absence of substrate. We investigate the apo-AdK transition at the atomic level both with free-energy calculations and with our new dynamic importance sampling (DIMS) molecular dynamics method. DIMS is shown to sample biologically relevant conformations as verified by comparing an ensemble of hundreds of DIMS transitions to AdK crystal structure intermediates. The simulations reveal in atomic detail how hinge regions partially and intermittently unfold during the transition. Conserved salt bridges are seen to have important structural and dynamic roles; in particular, four ionic bonds that open in a sequential, zipper-like fashion and, thus, dominate the free-energy landscape of the transition are identified. Transitions between the closed and open conformations only have to overcome moderate free-energy barriers. Unexpectedly, the closed state and the open state encompass broad free-energy basins that contain conformations differing in domain hinge motions by up to 40°. The significance of these extended states is discussed in relation to recent experimental Förster resonance energy transfer measurements. Taken together, these results demonstrate how a small number of cooperative key interactions can shape the overall dynamics of an enzyme and suggest an “all-or-nothing” mechanism for the opening and closing of AdK. Our efficient DIMS molecular dynamics computer simulation approach can provide a detailed picture of a functionally important macromolecular transition and thus help to interpret and suggest experiments to probe the conformational landscape of dynamic proteins such as AdK.     

Loop and stem dynamics during RNA hairpin folding and unfolding

2-Aminopurine (2AP) is a fluorescent adenine analog that probes mainly base stacking in nucleic acids. We labeled the loop or the stem of the RNA hairpin gacUACGguc with 2AP to study folding thermodynamics and kinetics at both loci. Thermal melts and fast laser temperature jumps detected by 2AP fluorescence monitored the stability and folding/unfolding kinetics. The observed thermodynamic and kinetic traces of the stem and loop mutants, though strikingly different at a first glance, can be fitted to the same free-energy landscape. The differences between the two probe locations arise because base stacking decreases upon unfolding in the stem, whereas it increases in the loop. We conclude that 2AP is a conservative adenine substitution for mapping out the contributions of different RNA structural elements to the overall folding process. Molecular dynamics (MD) totaling 0.6 μsec were performed to look at the conformations populated by the RNA at different temperatures. The combined experimental data, and MD simulations lead us to propose a minimal four-state free-energy landscape for the RNA hairpin. Analysis of this landscape shows that a sequential folding model is a good approximation for the full folding dynamics. The frayed state formed initially from the native state is a heterogeneous ensemble of structures whose stem is frayed either from the end or from the loop.     

Molecular dynamics methods to predict peptide locations in membranes: LAH4 as a stringent test case

Determining the structure of membrane-active peptides inside lipid bilayers is essential to understand their mechanism of action. Molecular dynamics simulations can easily provide atomistic details, but need experimental validation. We assessed the reliability of self-assembling (or “minimum-bias”) and potential of mean force (PMF) approaches, using all-atom (AA) and coarse-grained (CG) force-fields. The LAH4 peptide was selected as a stringent test case, since it is known to attain different orientations depending on the protonation state of its four histidine residues.In all simulations the histidine side-chains inserted in the membrane when neutral, while they interacted with phospholipid headgroups in their charged state. This led to transmembrane orientations for neutral-His LAH4 in all minimum-bias AA simulations and in most CG trajectories. By contrast, the charged-His peptide stabilized membrane defects in AA simulations, whereas it was located at the membrane surface in some CG trajectories, and interacted with both lipid leaflets in others. This behavior is consistent with the higher antimicrobial activity and membrane-permeabilizing behavior of the charged-His LAH4. In addition, good agreement with solid-state NMR orientational data was observed in AA simulations.PMF calculations correctly predicted a higher membrane affinity for the neutral-His peptide. Interestingly, the structures and relative populations of PMF local free-energy minima corresponded to those determined in the less computationally demanding minimum-bias simulations.These data provide an indication about the possible membrane-perturbation mechanism of the charged-His LAH4 peptide: by interacting with lipid headgroups of both leaflets through its cationic side-chains, it could favor membrane defects and facilitate translocation across the bilayer.     

Multiscale modeling of nucleosome dynamics

Nucleosomes form the fundamental building blocks of chromatin. Subtle modifications of the constituent histone tails mediate chromatin stability and regulate gene expression. For this reason, it is important to understand structural dynamics of nucleosomes at atomic levels. We report a novel multiscale model of the fundamental chromatin unit, a nucleosome, using a simplified model for rapid discrete molecular dynamics simulations and an all-atom model for detailed structural investigation. Using a simplified structural model, we perform equilibrium simulations of a single nucleosome at various temperatures. We further reconstruct all-atom nucleosome structures from simulation trajectories. We find that histone tails bind to nucleosomal DNA via strong salt-bridge interactions over a wide range of temperatures, suggesting a mechanism of chromatin structural organization whereby histone tails regulate inter- and intranucleosomal assemblies via binding with nucleosomal DNA. We identify specific regions of the histone core H2A/H2B-H4/H3-H3/H4-H2B/H2A, termed “cold sites”, which retain a significant fraction of contacts with adjoining residues throughout the simulation, indicating their functional role in nucleosome organization. Cold sites are clustered around H3-H3, H2A-H4 and H4-H2A interhistone interfaces, indicating the necessity of these contacts for nucleosome stability. Essential dynamics analysis of simulation trajectories shows that bending across the H3-H3 is a prominent mode of intranucleosomal dynamics. We postulate that effects of salts on mononucleosomes can be modeled in discrete molecular dynamics by modulating histone-DNA interaction potentials. Local fluctuations in nucleosomal DNA vary significantly along the DNA sequence, suggesting that only a fraction of histone-DNA contacts make strong interactions dominating mononucleosomal dynamics. Our findings suggest that histone tails have a direct functional role in stabilizing higher-order chromatin structure, mediated by salt-bridge interactions with adjacent DNA.     

The energetics of T4 lysozyme reveal a hierarchy of conformations.

We have used native state exchange to examine the energy landscape of the well-characterized protein T4 lysozyme. Although the protein exhibits two-state behavior by traditional probes, the energy landscape determined here is much more complex. The average stability of the C-terminal subdomain is significantly higher than that for the N-terminus suggesting at least two regions of unfolding. At a more detailed level, there appears to be a broad continuum of stabilities throughout each region. The overall subdomain hierarchy of energies does not mirror data on the folding pathway for this protein, challenging the relationship between energy landscapes and folding trajectories.     

Understanding the roles of amino acid residues in tertiary structure formation of chignolin by using molecular dynamics simulation

Chignolin is a 10-residue peptide (GYDPETGTWG) that forms a stable beta-hairpin structure in water. However, its design template, GPM12 (GYDDATKTFG), does not have a specific structure. To clarify which amino acids give it the ability to form the beta-hairpin structure, we calculated the folding free-energy landscapes of chignolin, GPM12, and their chimeric peptides using multicanonical molecular dynamics (MD) simulation. Cluster analysis of the conformational ensembles revealed that the native structure of chignolin was the lowest in terms of free energy while shallow local minima were widely distributed in the free energy landscape of GPM12, in agreement with experimental observations. Among the chimeric peptides, GPM12(D4P/K7G) stably formed the same beta-hairpin structure as that of chignolin in the MD simulation. This was confirmed by nuclear magnetic resonance (NMR) spectroscopy. A comparison of the free-energy landscapes showed that the conformational distribution of the Asp3-Pro4 sequence was inherently biased in a way that is advantageous both to forming hydrogen bonds with another beta-strand and to initiating loop structure. In addition, Gly7 helps stabilize the loop structure by having a left-handed alpha-helical conformation. Such a conformation is necessary to complete the loop structure, although it is not preferred by other amino acids. Our results suggest that the consistency between the short-range interactions that determine the local geometries and the long-range interactions that determine the global structure is important for stable tertiary structure formation.     

Exploration of multi-state conformational dynamics and underlying global functional landscape of maltose binding protein

An increasing number of biological machines have been revealed to have more than two macroscopic states. Quantifying the underlying multiple-basin functional landscape is essential for understanding their functions. However, the present models seem to be insufficient to describe such multiple-state systems. To meet this challenge, we have developed a coarse grained triple-basin structure-based model with implicit ligand. Based on our model, the constructed functional landscape is sufficiently sampled by the brute-force molecular dynamics simulation. We explored maltose-binding protein (MBP) which undergoes large-scale domain motion between open, apo-closed (partially closed) and holo-closed (fully closed) states responding to ligand binding. We revealed an underlying mechanism whereby major induced fit and minor population shift pathways co-exist by quantitative flux analysis. We found that the hinge regions play an important role in the functional dynamics as well as that increases in its flexibility promote population shifts. This finding provides a theoretical explanation of the mechanistic discrepancies in PBP protein family. We also found a functional "backtracking" behavior that favors conformational change. We further explored the underlying folding landscape in response to ligand binding. Consistent with earlier experimental findings, the presence of ligand increases the cooperativity and stability of MBP. This work provides the first study to explore the folding dynamics and functional dynamics under the same theoretical framework using our triple-basin functional model.     

Probing force-induced unfolding intermediates of a single staphylococcal nuclease molecule and the effect of ligand binding

Single-molecule manipulation techniques have given experimental access to unfolding intermediates of proteins that are inaccessible in conventional experiments. A detailed characterization of the intermediates is a challenging problem that provides new possibilities for directly probing the energy landscape of proteins. We investigated single-molecule mechanical unfolding of a small globular protein, staphylococcal nuclease (SNase), using atomic force microscopy. The unfolding trajectories of the protein displayed sub-molecular and stochastic behavior with typical lengths corresponding to the size of the unfolded substructures. Our results support the view that the single protein unfolds along multiple pathways as suggested in recent theoretical studies. Moreover, we found the drastic change, caused by the ligand and inhibitor bindings, in the mechanical unfolding dynamics.