Using one-step perturbation to predict the folding equilibrium of differently stereochemically substituted β-peptides

The one-step perturbation technique is used to predict the folding equilibria for 16 peptides with different stereochemical side-chain substitutions through one or two long-time simulations, one of an unphysical reference state and another of one of the 16 peptides for which many folding events can be sampled. The accuracy of the one-step perturbation results was investigated by comparing to results available from long-time MD simulations of particular peptides. Their folding free energies were reproduced within statistical accuracy. The one-step perturbation results show that an axial substitution at either the C(α) or the C(β) position destabilizes the 3(14)-helical conformation of the hepta-β-peptide, which is consistent with data inferred from experimental CD spectra. The methodology reduces the number of required separate simulations by an order of magnitude.     

On the influence of charged side chains on the folding-unfolding equilibrium of beta-peptides: a molecular dynamics simulation study

The influence of charged side chains on the folding-unfolding equilibrium of beta-peptides was investigated by means of molecular dynamics simulations. Four different peptides containing only negatively charged side chains, positively charged side chains, both types of charged side chains (with the ability to form stabilizing salt bridges) or no charged side chains were studied under various conditions (different simulation temperatures, starting structures and solvent environment). The NMR solution structure in methanol of one of the peptides (A) has already been published; the synthesis and NMR analysis of another peptide (B) is described here. The other peptides (C and D) studied herein have hitherto not been synthesized. All four peptides A-D are expected to adopt a left-handed 3(14)-helix in solution as well as in the simulations. The resulting ensembles of structures were analyzed in terms of conformational space sampled by the peptides, folding behavior, structural properties such as hydrogen bonding, side chain-side chain and side chain-backbone interactions and in terms of the level of agreement with the NMR data available for two of the peptides. It was found that the presence of charged side chains significantly slows down the folding process in methanol solution due to the stabilization of intermediate conformers with side chain-backbone interactions. In water, where the solvent competes with the solute-solute polar interactions, the folding process to the 3(14)-helix is faster in the simulations.     

Efficient molecular mechanics simulations of the folding,orientation, and assembly of peptides in lipid bilayers using an implicit atomic solvation model

Membrane proteins comprise a significant fraction of the proteomes of sequenced organisms and are the targets of approximately half of marketed drugs. However, in spite of their prevalence and biomedical importance, relatively few experimental structures are available due to technical challenges. Computational simulations can potentially address this deficit by providing structural models of membrane proteins. Solvation within the spatially heterogeneous membrane/solvent environment provides a major component of the energetics driving protein folding and association within the membrane. We have developed an implicit solvation model for membranes that is both computationally efficient and accurate enough to enable molecular mechanics predictions for the folding and association of peptides within the membrane. We derived the new atomic solvation model parameters using an unbiased fitting procedure to experimental data and have applied it to diverse problems in order to test its accuracy and to gain insight into membrane protein folding. First, we predicted the positions and orientations of peptides and complexes within the lipid bilayer and compared the simulation results with solid-state NMR structures. Additionally, we performed folding simulations for a series of host–guest peptides with varying propensities to form alpha helices in a hydrophobic environment and compared the structures with experimental measurements. We were also able to successfully predict the structures of amphipathic peptides as well as the structures for dimeric complexes of short hexapeptides that have experimentally characterized propensities to form beta sheets within the membrane. Finally, we compared calculated relative transfer energies with data from experiments measuring the effects of mutations on the free energies of translocon-mediated insertion of proteins into lipid bilayers and of combined folding and membrane insertion of a beta barrel protein.     

Single-molecule electrophoresis of beta-hairpin peptides by electrical recordings and Langevin dynamics simulations

We used single-channel electrical recordings and Langevin molecular dynamics simulations to explore the electrophoretic translocation of various beta-hairpin peptides across the staphylococcal alpha-hemolysin (alphaHL) protein pore at single-molecule resolution. The beta-hairpin peptides, which varied in their folding properties, corresponded to the C terminal residues of the B1 domain of protein G. The translocation time was strongly dependent on the electric force and was correlated with the folding features of the beta-hairpin peptides. Highly unfolded peptides entered the pore in an extended conformation, resulting in fast single-file translocation events. In contrast, the translocation of the folded beta-hairpin peptides occurred more slowly. In this case, the beta-hairpin peptides traversed the alphaHL pore in a misfolded or fully folded conformation. This study demonstrates that the interaction between a polypeptide and a beta-barrel protein pore is dependent on the folding features of the polypeptide.     

Peptide folding using multiscale coarse-grained models

The multiscale coarse-graining (MS-CG) method has been previously used to describe the equilibrium properties of peptides. The present study reveals that MS-CG models of alpha-helical polyalanine and the beta-hairpin V 5PGV 5 possess the capacity to efficiently refold in simulations initiated from unfolded configurations. The MS-CG peptides exhibit free energy landscapes that are funneled toward folded configurations and two-state folding behavior, consistent with the known characteristics of small, rapidly folding peptides. Moreover, the models demonstrate enhanced sampling capabilities when compared to systems with full atomic detail. The significance of these observations with respect to the theoretical basis of the MS-CG approach is discussed. The MS-CG peptides were used to reconstruct atomically detailed configurations in order to evaluate the extent to which MS-CG ensembles embody all-atom peptide free energy landscapes. Ensembles obtained from these reconstructed configurations display good agreement with the all-atom simulation data used to generate the MS-CG models and also corroborate the presence of features observed in the MS-CG peptide free energy landscapes. These findings suggest that MS-CG models may be of significant utility in the study of peptide folding.     

How Photoisomerization Drives Peptide Folding and Unfolding: Insights from QM/MM and MM Dynamics Simulations

Photoswitchable azobenzene cross‐linkers can control the folding and unfolding of peptides by photoisomerization and can thus regulate peptide affinities and enzyme activities. Using quantum mechanics/molecular mechanics (QM/MM) methods and classical MM force fields, we report the first molecular dynamics simulations of the photoinduced folding and unfolding processes in the azobenzene cross‐linked FK‐11 peptide. We find that the interactions between the peptide and the azobenzene cross‐linker are crucial for controlling the evolution of the secondary structure of the peptide and responsible for accelerating the folding and unfolding events. They also modify the photoisomerization mechanism of the azobenzene cross‐linker compared with the situation in vacuo or in solution.     

Do Valine Side Chains Have an Influence on the Folding Behavior of β‐Substituted β‐Peptides?

The influence of valine side chains on the folding/unfolding equilibrium and, in particular, on the 3₁₄‐helical propensity of β³‐peptides were investigated by means of molecular‐dynamics (MD) simulation. To that end, the valine side chains in two different β³‐peptides were substituted by leucine side chains. The resulting four peptides, of which three have never been synthesized, were simulated for 150 to 200 ns at 298 and 340 K, starting from a fully extended conformation. The simulation trajectories obtained were compared with respect to structural preferences and folding behavior. All four peptides showed a similar folding behavior and were found to predominantly adopt 3₁₄‐helical conformations, irrespective of the presence of valine side chains. No other well‐defined conformation was observed at significant population in any of the simulations. Our results imply that β³‐peptides show a structural preference for 3₁₄‐helices independent of the branching nature of the side chains, in contrast to what has been previously proposed on the basis of circular‐dichroism (CD) measurements.     

Influence of temperature, friction, and random forces on folding of the B-domain of staphylococcal protein A: all-atom molecular dynamics in implicit solvent

The influences of temperature, friction, and random forces on the folding of protein A have been analyzed. A series of all-atom molecular dynamics folding simulations with the Amber ff99 potential and Generalized Born solvation, starting from the fully extended chain, were carried out for temperatures from 300 to 500 K, using (a) the Berendsen thermostat (with no explicit friction or random forces) and (b) Langevin dynamics (with friction and stochastic forces explicitly present in the system). The simulation temperature influences the relative time scale of the major events on the folding pathways of protein A. At lower temperatures, helix 2 folds significantly later than helices 1 and 3. However, with increasing temperature, the folding time of helix 2 approaches the folding times of helices 1 and 3. At lower temperatures, the complete formation of secondary and tertiary structure is significantly separated in time whereas, at higher temperatures, they occur simultaneously. These results suggest that some earlier experimental and theoretical observations of folding events, e.g., the order of helix formation, could depend on the temperature used in those studies. Therefore, the differences in temperature used could be one of the reasons for the discrepancies among published experimental and computational studies of the folding of protein A. Friction and random forces do not change the folding pathway that was observed in the simulations with the Berendsen thermostat, but their explicit presence in the system extends the folding time of protein A.     

Folding Dynamics of 10‐Residue β‐Hairpin Peptide Chignolin

Short peptides that fold into β‐hairpins are ideal model systems for investigating the mechanism of protein folding because their folding process shows dynamics typical of proteins. We performed folding, unfolding, and refolding molecular dynamics simulations (total of 2.7 μs) of the 10‐residue β‐hairpin peptide chignolin, which is the smallest β‐hairpin structure known to be stable in solution. Our results revealed the folding mechanism of chignolin, which comprises three steps. First, the folding begins with hydrophobic assembly. It brings the main chain together; subsequently, a nascent turn structure is formed. The second step is the conversion of the nascent turn into a tight turn structure along with interconversion of the hydrophobic packing and interstrand hydrogen bonds. Finally, the formation of the hydrogen‐bond network and the complete hydrophobic core as well as the arrangement of side‐chain–side‐chain interactions occur at approximately the same time. This three‐step mechanism appropriately interprets the folding process as involving a combination of previous inconsistent explanations of the folding mechanism of the β‐hairpin, that the first event of the folding is formation of hydrogen bonds and the second is that of the hydrophobic core, or vice versa.     

Peptide loop-closure kinetics from microsecond molecular dynamics simulations in explicit solvent

End-to-end contact formation rates of several peptides were recently measured by tryptophan triplet quenching (Lapidus et al. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 7220). Motivated by these experiments, we study loop-closure kinetics for two peptides of different lengths, Cys-(Ala-Gly-Gln)n-Trp (n = 1, 2), in multiple all-atom explicit-solvent molecular dynamics simulations with different initial conditions and force fields. In 150 simulations of approximately 20 ns each, we collect data covering 1.0 and 0.8 micros for the penta-peptide simulated with the AMBER and CHARMM force fields, respectively, and about 0.5 micros each with the two force fields for the octa-peptide. These extensive simulations allow us to analyze the dynamics of peptides in the unfolded state with atomic resolution, thus probing early events in protein folding, and to compare molecular dynamics simulations directly with experiment. The calculated lifetimes of the tryptophan triplet state are in the range of 50-100 ns, in agreement with experimental measurements. However, end-to-end contacts form more rapidly, with characteristic times less than 10 ns. The contact formation rates for the two force fields are similar despite differences in the respective ensembles of peptide conformations.     

Numerical comparisons of three recently proposed algorithms in the protein folding problem

We numerically compare the effectiveness of three recently proposed algorithms, multicanonical algorithm, simulations in a 1/k-sampling, and simulated tempering, for the protein folding problem. We perform simulations with high statistics for one of the simplest peptides, met-enkephalin. While the performances of all three approaches is much better than traditional methods, we find that the differences among the three are only marginal. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 920–933, 1997     

Pathways to folding, nucleation events, and native geometry

We perform extensive Monte Carlo simulations of a lattice model and the Gō potential [N. Gō and H. Taketomi, Proc. Natl. Acad. Sci. U.S.A. 75, 559563 (1978)] to investigate the existence of folding pathways at the level of contact cluster formation for two native structures with markedly different geometries. Our analysis of folding pathways revealed a common underlying folding mechanism, based on nucleation phenomena, for both protein models. However, folding to the more complex geometry (i.e., that with more nonlocal contacts) is driven by a folding nucleus whose geometric traits more closely resemble those of the native fold. For this geometry folding is clearly a more cooperative process.     

Relationship between side chain structure and 14-helix stability of beta3-peptides in water

Folded polymers are used in Nature for virtually every vital process. Nonnatural folded polymers, or foldamers, have the potential for similar versatility, and the design and refinement of such molecules is of considerable current interest. Here we report a complete and systematic analysis of the relationship between side chain structure and the 14-helicity of a well-studied class of foldamers, beta(3)-peptides, in water. Our experimental results (1) verify the importance of macrodipole stabilization for maintaining 14-helix structure, (2) provide comprehensive evidence that beta(3)-amino acids branched at the first side chain carbon are 14-helix-stabilizing, (3) suggest a novel role for side chain hydrogen bonding as an additional stabilizing force in beta(3)-peptides containing beta(3)-homoserine or beta(3)-homothreonine, and (4) demonstrate that diverse functionality can be incorporated into a stable 14-helix. Gas- and solution-phase calculations and Monte Carlo simulations recapitulate the experimental trends only in the context of oligomers, yielding insight into the mechanisms behind 14-helix folding. The 14-helix propensities of beta(3)-amino acids differ starkly from the alpha-helix propensities of analogous alpha-amino acids. This contrast informs current models for alpha-helix folding, and suggests that 14-helix folding is governed by different biophysical forces than is alpha-helix folding. The ability to modulate 14-helix structure through side chain choice will assist rational design of 14-helical beta-peptide ligands for macromolecular targets.     

Theoretical characterization of alpha-helix and beta-hairpin folding kinetics

By means of the conformational free energy surface and corresponding diffusion coefficients, as obtained by long time scale atomistic molecular dynamics simulations (mus time scale), we model the folding kinetics of alpha-helix and beta-hairpin peptides as a diffusive process over the free energy surface. The two model systems studied in this paper (the alpha-helical temporin L and the beta-hairpin prion protein H1 peptide) exhibit a funnel-like almost barrierless free energy profile, leading to nonexponential folding kinetics matching rather well the available experimental data. Moreover, using the free energy profile provided by Mu?oz et al. [Mu?oz et al. Nature 1997, 390: 196-199], this model was also applied to reproduce the two-state folding kinetics of the C-terminal beta-hairpin of protein GB1, yielding an exponential folding kinetics with a time constant (approximately 5 micros) in excellent agreement with the experimentally observed one (approximately 6 micros). Finally, the folding kinetics obtained by solving the diffusion equation, considering either a one-dimensional or a two-dimensional free energy surface, are also compared in order to understand the relevance of the possible kinetic coupling between conformational degrees of freedom in the folding process.     

The Thermodynamics of Folding of a β Hairpin Peptide Probed Through Replica Exchange Molecular Dynamics Simulations

Peptides that possess a well defined native state are ideal model systems to study the folding of proteins. They possess many of the complexities of larger proteins, yet their small size renders their study computationally tractable. Recent advances in sampling techniques, including replica exchange molecular dynamics, now permit a full characterization of the thermodynamics of folding of small peptides. These simulations not only yield insight into the folding of larger proteins, but equally importantly, they allow, through comparison with experiment, an objective test of the accuracy of force fields, water models and of different numerical schemes for dealing with electrostatic interactions. In this account, we present a molecular dynamics simulation of a small β-hairpin peptide using the replica exchange algorithm and illustrate how this enhanced sampling scheme enables a thorough characterization of the native and unfolded states, and sheds new light into its folding mechanism.     

Balancing solvation and intramolecular interactions: toward a consistent generalized Born force field

The efficient and accurate characterization of solvent effects is a key element in the theoretical and computational study of biological problems. Implicit solvent models, particularly generalized Born (GB) continuum electrostatics, have emerged as an attractive tool to study the structure and dynamics of biomolecules in various environments. Despite recent advances in this methodology, there remain limitations in the parametrization of many of these models. In the present work, we demonstrate that it is possible to achieve a balanced implicit solvent force field by further optimizing the input atomic radii in combination with adjusting the protein backbone torsional energetics. This parameter optimization is guided by the potentials of mean force (PMFs) between amino acid polar groups, calculated from explicit solvent free energy simulations, and by conformational equilibria of short peptides, obtained from extensive folding and unfolding replica exchange molecular dynamics (REX-MD) simulations. Through the application of this protocol, the delicate balance between the competing solvation forces and intramolecular forces appears to be better captured, and correct conformational equilibria for a range of both helical and beta-hairpin peptides are obtained. The same optimized force field also successfully folds both beta-hairpin trpzip2 and mini-protein Trp-Cage, indicating that it is quite robust. Such a balanced, physics-based force field will be highly applicable to a range of biological problems including protein folding and protein structural dynamics.     

Hamiltonian replica‐exchange simulations with adaptive biasing of peptide backbone and side chain dihedral angles

A Hamiltonian Replica‐Exchange Molecular Dynamics (REMD) simulation method has been developed that employs a two‐dimensional backbone and one‐dimensional side chain biasing potential specifically to promote conformational transitions in peptides. To exploit the replica framework optimally, the level of the biasing potential in each replica was appropriately adapted during the simulations. This resulted in both high exchange rates between neighboring replicas and improved occupancy/flow of all conformers in each replica. The performance of the approach was tested on several peptide and protein systems and compared with regular MD simulations and previous REMD studies. Improved sampling of relevant conformational states was observed for unrestrained protein and peptide folding simulations as well as for refinement of a loop structure with restricted mobility of loop flanking protein regions. © 2013 Wiley Periodicals, Inc.     

Evaluating force field accuracy with long-time simulations of a β-hairpin tryptophan zipper peptide

We have combined graphics processing unit-accelerated all-atom molecular dynamics with parallel tempering to explore the folding properties of small peptides in implicit solvent on the time scale of microseconds. We applied this methodology to the synthetic β-hairpin, trpzip2, and one of its sequence variants, W2W9. Each simulation consisted of over 8 μs of aggregated virtual time. Several measures of folding behavior showed good convergence, allowing comparison with experimental equilibrium properties. Our simulations suggest that the intramolecular interactions of tryptophan side chains are responsible for much of the stability of the native fold. We conclude that the ff99 force field combined with ff96 φ and ψ dihedral energies and an implicit solvent can reproduce plausible folding behavior in both trpzip2 and W2W9.