Amyloid beta-peptide oligomerization in silico: dimer and trimer

Soluble oligomers of Alzheimer's amyloid beta protein (Abeta) may act as effectors of neurotoxicity in early stages of Alzheimer's disease. Detailed information about the structure of Abeta in atomistic level and the dynamics of assembly of monomeric Abeta into oligomeric structures is rather elusive. We have performed replica exchange molecular dynamics (REMD) simulations on the formation of the dimer and trimer of Abeta10-35 peptide. We have observed spontaneous formation of several basic structural units that may act as a template or an intermediate for further aggregation of Alzheimer's Abeta protein. Various conformers, including interlocking structures of experimentally known bend double beta strands, are identified.     

Comparison of implicit solvent models for the simulation of protein-surface interactions

Empirical force field-based molecular simulations can provide valuable atomistic-level insights into protein-surface interactions in aqueous solution. While the implicit treatment of solvation effects is desired as a means of improving simulation efficiency, existing implicit solvent models were primarily developed for the simulation of peptide or protein behavior in solution alone, and thus may not be appropriate for protein interactions with synthetic material surfaces. The objective of this research was to calculate the change in free energy as a function of surface-separation distance for peptide-surface interactions using different empirical force field-based implicit solvation models (ACE, ASP, EEF1, and RDIE with the CHARMM 19 force field), and to compare these results with the same calculations conducted using density functional theory (DFT) combined with the self-consistent reaction field (SCRF) implicit solvation model. These comparisons show that distinctly different types of behavior are predicted with each implicit solvation method, with ACE providing the best overall agreement with DFT/SCRF calculations. These results also identify areas where ACE is in need of improvement for this application and provide a basis for subsequent parameter refinement.     

Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth-permittivity finite difference Poisson-Boltzmann method

A fast stable finite difference Poisson-Boltzmann (FDPB) model for implicit solvation in molecular dynamics simulations was developed using the smooth permittivity FDPB method implemented in the OpenEye ZAP libraries. This was interfaced with two widely used molecular dynamics packages, AMBER and CHARMM. Using the CHARMM-ZAP software combination, the implicit solvent model was tested on eight proteins differing in size, structure, and cofactors: calmodulin, horseradish peroxidase (with and without substrate analogue bound), lipid carrier protein, flavodoxin, ubiquitin, cytochrome c, and a de novo designed 3-helix bundle. The stability and accuracy of the implicit solvent simulations was assessed by examining root-mean-squared deviations from crystal structure. This measure was compared with that of a standard explicit water solvent model. In addition we compared experimental and calculated NMR order parameters to obtain a residue level assessment of the accuracy of MD-ZAP for simulating dynamic quantities. Overall, the agreement of the implicit solvent model with experiment was as good as that of explicit water simulations. The implicit solvent method was up to eight times faster than the explicit water simulations, and approximately four times slower than a vacuum simulation (i.e., with no solvent treatment).     

Annular structures as intermediates in fibril formation of Alzheimer Abeta17-42

We report all-atom molecular dynamics simulations of annular beta-amyloid (17-42) structures, single- and double-layered, in solution. We assess the structural stability and association force of Abeta annular oligomers associated through different interfaces, with a mutated sequence (M35A), and with the oxidation state (M35O). Simulation results show that single-layered annular models display inherent structural instability: one is broken down into linear-like oligomers, and the other collapses. On the other hand, a double-layered annular structure where the two layers interact through their C-termini to form an NC-CN interface (where N and C are the N and C termini, respectively) exhibits high structural stability over the simulation time due to strong hydrophobic interactions and geometrical constraints induced by the closed circular shape. The observed dimensions and molecular weight of the oligomers from atomic force microscopy (AFM) experiments are found to correspond well to our stable double-layered model with the NC-CN interface. Comparison with K3 annular structures derived from the beta 2-microglobulin suggests that the driving force for amyloid formation is sequence specific, strongly dependent on side-chain packing arrangements, structural morphologies, sequence composition, and residue positions. Combined with our previous simulations of linear-like Abeta, K3 peptide, and sup35-derived GNNQQNY peptide, the annular structures provide useful insight into oligomeric structures and driving forces that are critical in amyloid fibril formation.     

Computational study on the structural diversity of amyloid Beta Peptide (abeta(10-35)) oligomers

We studied the oligomerization of Alzheimer amyloid beta peptide (Abeta) using a replica exchange molecular dynamics (REMD) simulation. The simulation was performed with Abeta(10-35) dimers, trimers, and tetramers. Extensive REMD simulations illustrated several possible oligomer conformations. As the size of the oligomer increased from a dimer to a tetramer, the number of possible configurations was reduced. We identified all the possible conformations for each oligomer and characterized their temperature dependence. It was found that the detailed structures of the oligomers, which may act as folding intermediates, are highly sensitive to the parameters of the simulation environment such as temperature and concentration. Structural diversities of Abeta oligomers suggest multiple pathways of the aggregation process.     

Establishing effective simulation protocols for beta- and alpha/beta-peptides. II. Molecular mechanical (MM) model for a cyclic beta-residue

All-atom molecular mechanical (MM) force field parameters are developed for a cyclic beta-amino acid, amino-cyclo-pentane-carboxylic acid (ACPC), using a multi-objective evolutionary algorithm. The MM model is benchmarked using several short, ACPC-containing alpha/beta-peptides in water and methanol with SCC-DFTB (self consistent charge-density functional tight binding)/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC-DFTB/MM results regarding the distribution of key dihedral angles for the tetra-alpha/beta-peptide in water. For the octa-alpha/beta-peptide in methanol, the MM and SCC-DFTB/MM simulations predict the 11- and 14/15-helical form as the more stable conformation, respectively; however, the two helical forms are very close in energy (2-4 kcal/mol) at both theoretical levels, which is also the conclusion from recent NMR experiments. As the first application, the MM model is applied to an alpha/beta-pentadeca-peptide in water with both explicit and implicit solvent models. The stability of the peptide is sensitive to the starting configuration in the explicit solvent simulations due to their limited length ( approximately 10-40 ns). Multiple ( approximately 20 x 20 ns) implicit solvent simulations consistently show that the 14/15-helix is the predominant conformation of this peptide, although substantially different conformations are also accessible. The calculated nuclear Overhauser effect (NOE) values averaged over different trajectories are consistent with experimental data, which emphasizes the importance of considering conformational heterogeneity in such comparisons for highly dynamical peptides.     

Molecular dynamics study of peptides in implicit water: ab initio folding of beta-hairpin, beta-sheet, and beta beta alpha-motif

In this communication, we have demonstrated that molecular dynamics simulations using a GB implicit solvation model with the all-atom based force field (CHARMM19) can describe the spontaneous folding of small peptides in aqueous solution. The native structures of peptides with various structural motifs (beta-hairpin, beta-sheet, and betabetaalpha-moiety) were successfully predicted within reasonable time scales by MD simulations at moderately elevated temperatures. It is expected that the present simulations provide further insight into mechanism/pathways of the peptide folding.     

Comparison of solvation-effect methods for the simulation of peptide interactions with a hydrophobic surface

In this study we investigated the interaction behavior between thirteen different small peptides and a hydrophobic surface using three progressively more complex methods of representing solvation effects: a united-atom implicit solvation method [CHARMM 19 force field (C19) with Analytical Continuum Electrostatics (ACE)], an all-atom implicit solvation method (C22 with GBMV), and an all-atom explicit solvation method (C22 with TIP3P). The adsorption behavior of each peptide was characterized by the calculation of the potential of mean force as a function of peptide-surface separation distance. The results from the C22/TIP3P model suggest that hydrophobic peptides exhibit relatively strong adsorption behavior, polar and positively-charged peptides exhibit negligible to relatively weak favorable interactions with the surface, and negatively-charged peptides strongly resist adsorption. Compared to the TIP3P model, the ACE and GBMV implicit solvent models predict much stronger attractions for the hydrophobic peptides as well as stronger repulsions for the negatively-charged peptides on the CH(3)-SAM surface. These comparisons provide a basis from which each of these implicit solvation methods may be reparameterized to provide closer agreement with explicitly represented solvation in simulations of peptide and protein adsorption to functionalized surfaces.     

Comparison of Secondary Structure Formation Using 10 Different Force Fields in Microsecond Molecular Dynamics Simulations

We have compared molecular dynamics (MD) simulations of a β-hairpin forming peptide derived from the protein Nrf2 with 10 biomolecular force fields using trajectories of at least 1 μs. The total simulation time was 37.2 μs. Previous studies have shown that different force fields, water models, simulation methods, and parameters can affect simulation outcomes. The MD simulations were done in explicit solvent with a 16-mer Nrf2 β-hairpin forming peptide using Amber ff99SB-ILDN, Amber ff99SB*-ILDN, Amber ff99SB, Amber ff99SB*, Amber ff03, Amber ff03*, GROMOS96 43a1p, GROMOS96 53a6, CHARMM27, and OPLS-AA/L force fields. The effects of charge-groups, terminal capping, and phosphorylation on the peptide folding were also examined. Despite using identical starting structures and simulation parameters, we observed clear differences among the various force fields and even between replicates using the same force field. Our simulations show that the uncapped peptide folds into a native-like β-hairpin structure at 310 K when Amber ff99SB-ILDN, Amber ff99SB*-ILDN, Amber ff99SB, Amber ff99SB*, Amber ff03, Amber ff03*, GROMOS96 43a1p, or GROMOS96 53a6 were used. The CHARMM27 simulations were able to form native hairpins in some of the elevated temperature simulations, while the OPLS-AA/L simulations did not yield native hairpin structures at any temperatures tested. Simulations that used charge-groups or peptide capping groups were not largely different from their uncapped counterparts with single atom charge-groups. On the other hand, phosphorylation of the threonine residue located at the β-turn significantly affected the hairpin formation. To our knowledge, this is the first study comparing such a large set of force fields with respect to β-hairpin folding. Such a comprehensive comparison will offer useful guidance to others conducting similar types of simulations.     

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.     

Dynamics and fluidity of amyloid fibrils: a model of fibrous protein aggregates

A previous experimentally defined model for the fibril formed from the core residues of the beta-amyloid (Abeta) peptides of Alzheimer's disease, 10YEVHHQKLVFFAEDVGSNKGAIIGLM, Abeta(10-35) using spectroscopic and scattering analyses reports on the average structure, benefiting immensely from the homogeneous assembly of Abeta(10-35). However, the energetic constraints that contribute to fibril dynamics and stability remain poorly understood. Here we perform molecular dynamics simulations to extend the structural assignment by providing evidence for a dynamic average ensemble with transient backbone H-bonds and internal solvation contributing to the inherent stability of amyloid fibrils.     

Role of ions on structure and stability of a synthetic gramicidin ion channel in solution. A molecular dynamics study

We performed a molecular dynamics (MD) simulation to the investigate structure and stability of a synthetic gramicidin-like peptide in solution with and without ions. The starting structures of the MD simulations were taken from two recently solved NMR structures of this peptide in isotropic solution, which forms stable monomers or dimers in the presence or absence of ions, respectively. The monomeric structure is channel-like and is assumed to be stabilized by the presence of two Cs(+) ions bound in the channel, each one close to one channel entrance. In our MD simulations, we observed how the Cs(+) ions bind in the channel formed by the monomeric gramicidin-like peptide using implicit solvent and explicit ions with a concentration of 2 M. MD simulations were performed with and without explicit ions but with an implicit solvent model defined by the generalized Born approximation, which was used to mimic the dielectric properties of the solvent and to speed up the computations.     

Proton binding to proteins: pK(a) calculations with explicit and implicit solvent models

Ionizable residues play important roles in protein structure and activity, and proton binding is a valuable reporter of electrostatic interactions in these systems. We use molecular dynamics free energy simulations (MDFE) to compute proton pKa shifts, relative to a model compound in solution, for three aspartate side chains in two proteins. Simulations with explicit solvent and with an implicit, dielectric continuum solvent are reported. The implicit solvent simulations use the generalized Born (GB) model, which provides an approximate, analytical solution to Poisson's equation. With explicit solvent, the direction of the pKa shifts is correct in all three cases with one force field (AMBER) and in two out of three cases with another (CHARMM). For two aspartates, the dielectric response to ionization is found to be linear, even though the separate protein and solvent responses can be nonlinear. For thioredoxin Asp26, nonlinearity arises from the presence of two substates that correspond to the two possible orientations of the protonated carboxylate. For this side chain, which is partly buried and has a large pKa upshift, very long simulations are needed to correctly sample several slow degrees of freedom that reorganize in response to the ionization. Thus, nearby Lys57 rotates to form a salt bridge and becomes buried, while three waters intercalate along the opposite edge of Asp26. Such strong and anisotropic reorganization is very difficult to predict with Poisson-Boltzmann methods that only consider electrostatic interactions and employ a single protein structure. In contrast, MDFE with a GB dielectric continuum solvent, used for the first time for pKa calculations, can describe protein reorganization accurately and gives encouraging agreement with experiment and with the explicit solvent simulations.     

Binding structures of tri‐N‐acetyl‐β‐glucosamine in hen egg white lysozyme using molecular dynamics with a polarizable force field

Lysozyme is a well‐studied enzyme that hydrolyzes the β‐(1,4)‐glycosidic linkage of N‐acetyl‐β‐glucosamine (NAG)_n oligomers. The active site of hen egg‐white lysozyme (HEWL) is believed to consist of six subsites, A‐F that can accommodate six sugar residues. We present studies exploring the use of polarizable force fields in conjunction with all‐atom molecular dynamics (MD) simulations to analyze binding structures of complexes of lysozyme and NAG trisaccharide, (NAG)₃. MD trajectories are applied to analyze structures and conformation of the complex as well as protein–ligand interactions, including the hydrogen‐bonding network in the binding pocket. Two binding modes (ABC and BCD) of (NAG)₃ are investigated independently based on a fixed‐charge model and a polarizable model. We also apply molecular mechanics with generalized born and surface area (MM‐GBSA) methods based on MD using both nonpolarizable and polarizable force fields to compute binding free energies. We also study the correlation between root‐mean‐squared deviation and binding free energies of the wildtype and W62Y mutant; we find that for this prototypical system, approaches using the MD trajectories coupled with implicit solvent models are equivalent for polarizable and fixed‐charge models. © 2012 Wiley Periodicals, Inc.     

Establishing effective simulation protocols for β‐ and α/β‐peptides. III. Molecular mechanical model for acyclic β‐amino acids

All‐atom molecular mechanics (MM) force field parameters are developed for the backbone of acyclic β‐amino acid using an improved version of the multiobjective evolutionary algorithm (MOEA). The MM model is benchmarked using β³‐homo‐Alanine (β³‐hAla) diamide in water with SCC‐DFTB/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC‐DFTB/MM results regarding the distribution of key dihedral angles for the β³‐hAla diamide in water. The MM model is further applied to a β‐hepta‐peptide in methanol solution. The calculated NOE values and ³J coupling constants averaged over different trajectories are consistent with experimental data. By contrast, simulations using parameters directly transferred from the CHARMM22 force field for proteins lead to much worse agreement, which highlights the importance of careful parameterization for non‐natural peptides, for which the improved MOEA is particularly useful. Finally, as an initial application of the new force field parameters, the behaviors of a short random copolymer consisting of β amino acids in bulk solution and membrane/water interface are studied using a generalized Born implicit solvent model (GBSW). Results for four selected sequences show that segregation of hydrophobic and cationic groups occur easily at the membrane/solution interface for all sequences. The sequence that features alternating short blocks exhibits signs of lower stability at the interface compared to other sequences. These results confirm the hypothesis in recent experimental studies that β‐amino‐acid based random copolymers can develop a high degree of amphiphilicity without regular three‐dimensional structure. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Molecular dynamics study of the beta amyloid peptide of Alzheimer's disease and its divalent copper complexes

The Abeta1-42 monomer structure was assessed with a 790 ns molecular dynamics (MD) simulation, and the results were compared with the NMR experiment on Abeta10-35 and Abeta1-40. Previous theoretical work in a model of the His13-His14 region of Abeta defined the possible Cu(II) binding geometries at this site (Raffa et al. J. Biol. Inorg. Chem. 2005, 10, 887-902). MD simulations totalling almost 2 micros were also carried out on Cu(II)/Abeta1-42 systems, using the ab initio structures as templates for the copper binding site. This work finds that the copper-free Abeta1-42 system may stabilize after approximately 350 ns into a collapsed coil conformation, and we find good agreement with some, but not all, of the structural features determined experimentally for the Abeta10-35 and Abeta1-40 peptides. The results of the Cu(II)/Abeta1-42 systems are compared to the Cu(II)-free Abeta1-42 simulation.     

Modern protein force fields behave comparably in molecular dynamics simulations

Several molecular dynamics simulations were performed on three proteins--bovine apo-calbindin D9K, human interleukin-4 R88Q mutant, and domain IIA of bacillus subtilis glucose permease--with each of the AMBER94, CHARMM22, and OPLS-AA force fields as implemented in CHARMM. Structural and dynamic properties such as solvent-accessible surface area, radius of gyration, deviation from their respective experimental structures, secondary structure, and backbone order parameters are obtained from each of the 2-ns simulations for the purpose of comparing the protein portions of these force fields. For one of the proteins, the interleukin-4 mutant, two independent simulations were performed using the CHARMM22 force field to gauge the sensitivity of some of these properties to the specific trajectory. In general, the force fields tested performed remarkably similarly with differences on the order of those found for the two independent trajectories of interleukin-4 with CHARMM22. When all three proteins are considered together, no force field showed any consistent trend in variations for most of the properties monitored in the study.