Sampling efficiency in explicit and implicit membrane environments studied by peptide folding simulations

Efficient exploration of the conformational space of peptides embedded in biological membranes is vital to extract converged thermodynamic and kinetic data from simulation studies. Recently developed implicit membrane models promise vast increases in sampling efficiency compared to explicit membrane simulations, allowing for ab initio structure prediction and functional studies. In this study, a previously developed implicit membrane model, based on the generalized Born method, is compared to an explicit di‐palmitoyl‐phosphatidyl‐choline lipid bilayer and an octane slab membrane mimic. The complete folding process of a synthetic 16‐residue peptide is compared using these three setups. Since the comparison requires the entire folding pathway to be captured, individual simulations ranged up to 3 μs of MD. A quantitative sampling comparison using a wide range of performance metrics reveals that the implicit membrane model is at least 2 orders of magnitude more efficient than the simplest explicit setups. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Beta-hairpin folding mechanism of a nine-residue peptide revealed from molecular dynamics simulations in explicit water

The beta-hairpin fold mechanism of a nine-residue peptide, which is modified from the beta-hairpin of alpha-amylase inhibitor tendamistat (residues 15-23), is studied through direct folding simulations in explicit water at native folding conditions. Three 300-nanosecond self-guided molecular dynamics (SGMD) simulations have revealed a series of beta-hairpin folding events. During these simulations, the peptide folds repeatedly into a major cluster of beta-hairpin structures, which agree well with nuclear magnetic resonance experimental observations. This major cluster is found to have the minimum conformational free energy among all sampled conformations. This peptide also folds into many other beta-hairpin structures, which represent some local free energy minimum states. In the unfolded state, the N-terminal residues of the peptide, Tyr-1, Gln-2, and Asn-3, have a confined conformational distribution. This confinement makes beta-hairpin the only energetically favored structure to fold. The unfolded state of this peptide is populated with conformations with non-native intrapeptide interactions. This peptide goes through fully hydrated conformations to eliminate non-native interactions before folding into a beta-hairpin. The folding of a beta-hairpin starts with side-chain interactions, which bring two strands together to form interstrand hydrogen bonds. The unfolding of the beta-hairpin is not simply the reverse of the folding process. Comparing unfolding simulations using MD and SGMD methods demonstrate that SGMD simulations can qualitatively reproduce the kinetics of the peptide system.     

Implicit solvent simulations of peptide interactions with anionic lipid membranes

A recently developed implicit membrane model (IMM1) is supplemented with a Gouy-Chapman term describing counterion-screened electrostatic interactions of a solute with negatively charged membrane lipids. The new model is tested on peptides that bind to anionic membranes. Pentalysine binds just outside the plane of negative charge, whereas Lys-Phe peptides insert their aromatic rings into the hydrophobic core. Melittin and magainin 2 bind more strongly to anionic than to neutral membranes and in both cases insert their hydrophobic residues into the hydrocarbon core. The third domain of Antennapedia homeodomain (penetratin) binds as an alpha-helix in the headgroup region. Cardiotoxin II binds strongly to anionic membranes but marginally to neutral ones. In all cases, the location and configuration of the peptides are consistent with experimental data, and the effective energy changes upon binding compare favorably with experimental binding free energies. The model opens the way to exploring the effect of membrane charge on the location, conformation, and dynamics of a large variety of biologically active peptides on membranes.     

Mechanical stability of helical beta-peptides and a comparison of explicit and implicit solvent models

Synthetic β-peptide oligomers have been shown to form stable folded structures analogous to those encountered in naturally occurring proteins. Literature studies have speculated that the conformational stability of β-peptides is greater than that of α-peptides. Direct measurements of that stability, however, are not available. Molecular simulations are used in this work to quantify the mechanical stability of four helical β-peptides. This is achieved by subjecting the molecules to tension. The potential of mean force associated with the resulting unfolding process is determined using both an implicit and an explicit solvent model. It is found that all four molecules exhibit a highly stable helical structure. It is also found that the energetic contributions to the potential of mean force do not change appreciably when the molecules are stretched in explicit water. In contrast, the entropic contributions decrease significantly. As the peptides unfold, a loss of intramolecular energy is compensated by the formation of additional water-peptide hydrogen bonds. These entropic effects lead in some cases to a loss of stability upon cooling the peptides, a phenomenon akin to the cold denaturing of some proteins. While the location of the free energy minimum and the structural helicity of the peptides are comparable in the implicit-solvent and explicit-water cases, it is found that, in general, the helical structure of the molecules is more stable in the implicit solvent model than in explicit water.     

Helix conformation of a small peptide melittin in a methanol-water mixed solvent studied by NMR

Temperature dependence of the α-helix conformation of bee venom melittin in methanol-water mixed solvents has been examined by NMR, in order to elucidate conformation stability and a phase diagram. At high methanol concentration of 100 - ca. 80 wt.%, melittin forms a full α-helix conformation in the temperature range from 25 °C to 60 °C. At intermediate methanol concentration of ca. 80 - ca. 25 wt.%, it undergoes a thermal transformation from a full α-helix to a partial α-helix. In solutions of low methanol concentrations of ca. 25 - 0 wt.%, partial α-helix monomers and their self-aggregated conformers coexist at low temperatures, and the relative number of the monomers increases with increase in temperature. The monomers turn to a random coil state at high temperatures only below ca. 10 wt. % methanol concentrations. The thermal transitions are discussed from the viewpoint of stability of intra-molecular hydrogen bonds and inter-molecular hydrophobic interactions.     

Mechanism of collagen folding propagation studied by Molecular Dynamics simulations

Collagen forms a characteristic triple helical structure and plays a central role for stabilizing the extra-cellular matrix. After a C-terminal nucleus formation folding proceeds to form long triple-helical fibers. The molecular details of triple helix folding process is of central importance for an understanding of several human diseases associated with misfolded or unstable collagen fibrils. However, the folding propagation is too rapid to be studied by experimental high resolution techniques. We employed multiple Molecular Dynamics simulations starting from unfolded peptides with an already formed nucleus to successfully follow the folding propagation in atomic detail. The triple helix folding was found to propagate involving first two chains forming a short transient template. Secondly, three residues of the third chain fold on this template with an overall mean propagation of ~75 ns per unit. The formation of loops with multiples of the repeating unit was found as a characteristic misfolding event especially when starting from an unstable nucleus. Central Gly→Ala or Gly→Thr substitutions resulted in reduced stability and folding rates due to structural deformations interfering with folding propagation.     

Folding mechanism of beta-hairpins studied by replica exchange molecular simulations

The folding process of trpzip2 beta-hairpin is studied by the replica exchange molecular dynamics (REMD) and normal MD simulations, aiming to understand the folding mechanism of this unique small, stable, and fast folder, as well as to reveal the general principles in the folding of beta-hairpins. According to our simulations, the TS ensemble is mainly characterized by a largely formed turn and the interaction between the inner pair of hydrophobic core residues. The folding is a zipping up of hydrogen bonds. However, the nascent turn has to be stabilized by the partially formed hydrophobic core to cross the TS. Thus our folding picture is in essence a blend of hydrogen bond-centric and hydrophobic core-centric mechanism. Our simulations provide a direct evidence for a very recent experiment (Du et al., Proc Natl Acad Sci USA 2004;101:15915-15920), which suggests that the turn formation is the rate-limiting step for beta-hairpin folding and the unfolding is mainly determined by the hydrophobic interactions. Besides, the relationship between hydrogen bond stabilities and their relative importance in folding are investigated. It is found that the hydrogen bonds with higher stabilities need not play more important roles in the folding process, and vice versa.     

Role of water on unfolding kinetics of helical peptides studied by molecular dynamics simulations

Molecular dynamics simulations have been carried out with four polypeptides, Ala13, Val(13), Ser13, and Ala4Gly5Ala4, in vacuo and with explicit hydration. The unfolding of the polypeptides, which are initially fully alpha-helix in conformation, has been monitored during trajectories of 0.3 ns at 350 K. A rank of Ala < Val < Ser < Gly is found in the order of increasing rate of unwinding. The unfolding of Ala13 and Val(13) is completed in hundreds of picoseconds, while that of Ser13 is about one order of magnitude faster. The helix content of the peptide containing glycine residues falls to zero within a few picoseconds. Ramachandran plots indicate quite distinct equilibrium distributions and time evolution of dihedral angles in water and in vacuum for each residue type. The unfolding of polyalanine and polyvaline helices is accelerated due to solvation. In contrast, polyserine is more stable in water compared to vacuum, because its side chains can form intramolecular hydrogen bonds with the backbone more readily in vacuum, which disrupts the helix. Distribution functions of the spatial and angular position of water molecules in the proximity of the polypeptide backbone polar groups reveal the stabilization of the coiled structures by hydration. The transition from helix to coil is characterized by the appearance of a new peak in the probability distribution at a specific location characteristic of hydrogen bond formation between water and backbone polar groups. No significant insertion of water molecules is observed at the precise onset of unwinding, while (i, i+3) hydrogen bond formation is frequently detected at the initiation of alpha-helix unwinding.     

The structure of the Alzheimer amyloid beta 10-35 peptide probed through replica-exchange molecular dynamics simulations in explicit solvent

The conformational states sampled by the Alzheimer amyloid beta (10-35) (Abeta 10-35) peptide were probed using replica-exchange molecular dynamics (REMD) simulations in explicit solvent. The Abeta 10-35 peptide is a fragment of the full-length Abeta 40/42 peptide that possesses many of the amyloidogenic properties of its full-length counterpart. Under physiological temperature and pressure, our simulations reveal that the Abeta 10-35 peptide does not possess a single unique folded state. Rather, this peptide exists as a mixture of collapsed globular states that remain in rapid dynamic equilibrium with each other. This conformational ensemble is dominated by random coil and bend structures with insignificant presence of an alpha-helical or beta-sheet structure. The 3D structure of Abeta 10-35 is seen to be defined by a salt bridge formed between the side-chains of K28 and D23. This salt bridge is also observed in Abeta fibrils and our simulations suggest that monomeric conformations of Abeta 10-35 contain pre-folded structural motifs that promote rapid aggregation of this peptide.     

Folding of a DNA hairpin loop structure in explicit solvent using replica-exchange molecular dynamics simulations

Hairpin loop structures are common motifs in folded nucleic acids. The 5'-GCGCAGC sequence in DNA forms a characteristic and stable trinucleotide hairpin loop flanked by a two basepair stem helix. To better understand the structure formation of this hairpin loop motif in atomic detail, we employed replica-exchange molecular dynamics (RexMD) simulations starting from a single-stranded DNA conformation. In two independent 36 ns RexMD simulations, conformations in very close agreement with the experimental hairpin structure were sampled as dominant conformations (lowest free energy state) during the final phase of the RexMDs ( approximately 35% at the lowest temperature replica). Simultaneous compaction and accumulation of folded structures were observed. Comparison of the GCA trinucleotides from early stages of the simulations with the folded topology indicated a variety of central loop conformations, but arrangements close to experiment that are sampled before the fully folded structure also appeared. Most of these intermediates included a stacking of the C(2) and G(3) bases, which was further stabilized by hydrogen bonding to the A(5) base and a strongly bound water molecule bridging the C(2) and A(5) in the DNA minor groove. The simulations suggest a folding mechanism where these intermediates can rapidly proceed toward the fully folded hairpin and emphasize the importance of loop and stem nucleotide interactions for hairpin folding. In one simulation, a loop motif with G(3) in syn conformation (dihedral flip at N-glycosidic bond) accumulated, resulting in a misfolded hairpin. Such conformations may correspond to long-lived trapped states that have been postulated to account for the folding kinetics of nucleic acid hairpins that are slower than expected for a semiflexible polymer of the same size.     

Molecular dynamics simulations of DNA and a protein-DNA complex including solvent

The results of a recent nanosecond (ns) molecular dynamics (MD) simulation of the d(CGCGAATTCGCG) double helix in water and a 100 ps MD study of the repressor-operator complex are described. The DNA simulations are analyzed in terms of the structural dynamics, fluctuations in the groove width and bending of the helical axis. The results indicate that the ns dynamical trajectory progresses through a series of three substates of B form DNA, with lifetimes of the order of hundreds of picoseconds (ps). An incipient dynamical equilibrium is evident. A comparison of the calculated axis bending with that observed in corresponding crystal structure data is presented. Simulation of the DNA in complex with the protein and that of the free DNA in solution, starting from the crystal conformation, reveal the dynamical changes that occur on complex formation.     

Cooperative folding mechanism of a beta-hairpin peptide studied by a multicanonical replica-exchange molecular dynamics simulation

G-peptide is a 16-residue peptide of the C-terminal end of streptococcal protein G B1 domain, which is known to fold into a specific beta-hairpin within 6 micros. Here, we study molecular mechanism on the stability and folding of G-peptide by performing a multicanonical replica-exchange (MUCAREM) molecular dynamics simulation with explicit solvent. Unlike the preceding simulations of the same peptide, the simulation was started from an unfolded conformation without any experimental information on the native conformation. In the 278-ns trajectory, we observed three independent folding events. Thus MUCAREM can be estimated to accelerate the folding reaction more than 60 times than the conventional molecular dynamics simulations. The free-energy landscape of the peptide at room temperature shows that there are three essential subevents in the folding pathway to construct the native-like beta-hairpin conformation: (i) a hydrophobic collapse of the peptide occurs with the side-chain contacts between Tyr45 and Phe52, (ii) then, the native-like turn is formed accompanying with the hydrogen-bonded network around the turn region, and (iii) finally, the rest of the backbone hydrogen bonds are formed. A number of stable native hydrogen bonds are formed cooperatively during the second stage, suggesting the importance of the formation of the specific turn structure. This is also supported by the accumulation of the nonnative conformations only with the hydrophobic cluster around Tyr45 and Phe52. These simulation results are consistent with high phi-values of the turn region observed by experiment.     

Salt effects on hydrophobic‐core formation in folding of a helical miniprotein studied by molecular dynamics simulations

We have investigated effects of salt ions on folding events of a helical miniprotein chicken villin headpiece subdomain HP36. Low concentrations of ions alter electrostatic interactions between charged groups of a protein and can change the populations of conformers. Here, we compare two data sets of folding simulations of HP36 in explicit water solvent with or without ions. For efficient sampling of the conformational space of HP36, the multicanonical replica‐exchange molecular dynamics method was employed. Our analyses suggest that salt alters salt‐bridging nature of the protein at later stages of folding at room temperature. Especially, more nonnative, nonlocal salt bridges are formed at near‐native conformations in pure water. Our analyses also show that such salt‐bridge formation hinders the fully native hydrophobic‐core packing at the final stages of folding. Proteins 2014; 82:933–943. © 2013 Wiley Periodicals, Inc.     

Anti-insulin antibody structure and conformation. II. Molecular dynamics with explicit solvent.

Molecular dynamics at 300 K was used as a conformation searching tool to analyze a knowledge-based structure prediction of an anti-insulin antibody. Solvation effects were modeled by packing water molecules around the antigen binding loops. Some loops underwent backbone and side-chain conformational changes during the 95-ps equilibration, and most of these new, lower potential energy conformations were stable during the subsequent 200-ps simulation. Alterations to the model include changes in the intraloop, main-chain hydrogen bonding network of loop H3, and adjustments of Tyr and Lys side chains of H3 induced by hydrogen bonding to water molecules. The structures observed during molecular dynamics support the conclusion of the previous paper that hydrogen bonding will play the dominant role in antibody-insulin recognition. Determination of the structure of the antibody by x-ray crystallography is currently being pursued to provide an experimental test of these results. The simulation appears to improve the model, but longer simulations at higher temperatures should be performed.     

Dependence on the dielectric model and pH in a synthetic helical peptide studied by Monte Carlo simulated annealing

Monte Carlo simulated annealing is applied to the tertiary structure prediction of a 17-residue synthetic peptide, which is known by experiment to exhibit high helical content at low pH. Two dielectric models are considered: sigmoidal distance-dependent dielectric function and a constant dielectric function (? = 2). Starting from completely random initial conformations, our simulations for both dielectric models at low pH gave many helical conformations. The obtained low-energy conformations are compared with the nuclear Overhauser effect spectroscopy cross-peak data for both main chain and side chains, and it is shown that the results for the sigmoidal dielectric function are in remarkable agreement with the experimental data. The results predict the existence of two disjoint helices around residues 5–9 and 11–16, while nmr experiments imply significant α-helix content between residues 5 and 14. Simulations with high pH, on the other hand, hardly gave a helical conformation, which is also in accord with the experiment. These findings indicate that when side chains are charged, electrostatic interactions due to these charges play a major role in the helix stability. Our results are compared with the previous 500 ps molecular dynamics simulations of the same peptide. It is argued that simulated annealing is superior to molecular dynamics in two respects: (1) direct folding of α-helix from completely random initial conformations is possible for the former, whereas only unfolding of an α-helix can be studied by the latter; (2) while both methods predict high helix content for low pH, the results for high pH agree with experiment (low helix content) only for the former method. © 1994 John Wiley & Sons, Inc.     

Molecular dynamics simulations of a fibrillogenic peptide derived from apolipoprotein C-II

The pathway to amyloid fibril formation in proteins involves specific structural changes leading to the combination of misfolded intermediates into oligomeric assemblies. Recent NMR studies showed the presence of “turns” in amyloid peptides, indicating that turn formation may play an important role in the nucleation of the intramolecular folding and possible assembly of amyloid. Fully solvated all-atom molecular dynamics simulations were used to study the structure and dynamics of the apolipoprotein C-II peptide 56 to 76, associated with the formation of amyloid fibrils. The peptide populated an ensemble of turn structures, stabilized by hydrogen bonds and hydrophobic interactions enabling the formation of a strong hydrophobic core which may provide the conditions required to initiate aggregation. Two competing mechanisms discussed in the literature were observed. This has implications in understanding the mechanism of amyloid formation in not only apoC-II and its fragments, but also in other amyloidogenic peptides.     

Molecular dynamics simulations of the ErbB-2 transmembrane domain within an explicit membrane environment: comparison with vacuum simulations

Two 500-ps molecular dynamics simulations performed on the single transmembrane domain of the ErbB-2 tyrosine kinase receptor immersed in a fully solvated dilauroylphosphatidyl-ethanolamine bilayer (DLPE) are compared to vacuum simulations. One membrane simulation shows that the initial alpha helix undergoes a local pi helix conversion in the peptide part embedded in the membrane core similar to that found in simulation vacuum. Lipid/water/peptide interaction analysis shows that in the helix core, the intramolecular peptide interactions are largely dominant compared to the interactions with water and lipids whereas the helix extremities are much more sensitive to these interactions at the membrane interfaces. Our results suggest that simulations in a lipid environment are required to understand the dynamics of transmembrane helices, but can be reasonably supplemented by in vacuo simulations to explore rapidly its conformational space and to describe the internal deformation of the hydrophobic core.     

Molecular dynamics simulations of folding processes of a beta-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.