Polypeptide Folding Using Monte Carlo Sampling, Concerted Rotation, and Continuum Solvation

Direct folding simulation of alpha-helices and beta-hairpins based on a single all-atom force field with an implicit solvation model

Recently, we have shown that a modified energy model based on the param99 force field with the generalized Born (GB) solvation model produces reliable free energy landscapes of mini-proteins with a betabetaalpha motif (BBA5, 1FSD, and 1PSV), with the native structures of the mini-proteins located in their lowest free energy minimum states. One of the main features in the modified energy model is a significant improvement for more balanced treatments of alpha and beta strands in proteins. In this study, using the replica exchange molecular dynamics (REMD) simulation method with this new force field, we have carried out extensive ab initio folding studies of several well-known peptides with alpha or beta strands (C-peptide, EK-peptide, le0q, and gbl). Starting from fully extended conformations as the initial conditions, all of the native-like structures of the target peptides were successfully identified by REMD, with reasonable representations of free energy surfaces. The present simulation results with the modified energy model are consistent with experiments, demonstrating an extended applicability of the energy model to folding studies of a variety of alpha-helices, beta-strands, and alpha/beta proteins.

A generalized born implicit-membrane representation compared to experimental insertion free energies

An implicit-membrane representation based on the generalized Born theory of solvation has been developed. The method was parameterized against the water-to-cyclohexane insertion free energies of hydrophobic side-chain analogs. Subsequently, the membrane was compared with experimental data from translocon inserted polypeptides and validated by comparison with an independent dataset of six membrane-associated peptides and eight integral membrane proteins of known structure and orientation. Comparison of the insertion energy of alpha-helical model peptides with the experimental values from the biological hydrophobicity scale of Hessa et al. gave a correlation of 93% with a mean unsigned error of 0.64 kcal/mol, when charged residues were ignored. The membrane insertion energy was found to be dependent on residue position. This effect is particularly pronounced for charged and polar residues, which strongly prefer interfacial locations. All integral membrane proteins investigated orient and insert correctly into the implicit-membrane model. Remarkably, the membrane model correctly predicts a partially inserted configuration for the monotopic membrane protein cyclooxygenase, matching experimental and theoretical predictions. To test the applicability and usefulness of the implicit-membrane method, molecular simulations of influenza A M2 as well as the glycophorin A dimer were performed. Both systems remain structurally stable and integrated into the membrane.

Folding and aggregation kinetics of a beta-hairpin

We have investigated the solution structure, equilibrium properties, and folding kinetics of a 17-residue beta-hairpin-forming peptide derived from the protein ubiquitin. NMR experiments show that at 4 degrees C the peptide has a highly populated beta-hairpin conformation. At protein concentrations higher than 0.35 mM, the peptide aggregates. Sedimentation equilibrium measurements show that the aggregate is a trimer, while NMR indicates that the beta-hairpin conformation is maintained in the trimer. The relaxation kinetics in nanosecond laser temperature-jump experiments reveal a concentration-independent microsecond phase, corresponding to beta-hairpin unfolding-refolding, and a concentration-dependent millisecond phase due to oligomerization. Kinetic modeling of the relaxation rates and amplitudes yields the folding and unfolding rates for the monomeric beta-hairpin, as well as assembly and disassembly rates for trimer formation consistent with the equilibrium constant determined by sedimentation equilibrium. When the net charge on the peptides and ionic strength were taken into account, the rate of trimer assembly approaches the Debye-Smoluchowski diffusion limit. At 300 K, the rate of formation of the monomeric hairpin is (17 micros)(-1), compared to rates of (0.8 micros)(-1) to (52 micros)(-1) found for other peptides. After using Kramers theory to correct for the temperature dependence of the pre-exponential factor, the activation energy for hairpin formation is near zero, indicating that the barrier to folding is purely entropic. Comparisons with previously measured rates for a series of hairpins are made to distinguish between zipper and hydrophobic collapse mechanisms. Overall, the experimental data are most consistent with the zipper mechanism in which structure formation is initiated at the turn, the mechanism predicted by the Ising-like statistical mechanical model that was developed to explain the equilibrium and kinetic data for the beta-hairpin from protein GB1. In contrast, the majority of simulation studies favor a hydrophobic collapse mechanism. However, with few exceptions, there is little or no quantitative comparison of the simulation results with experimental data.

Exploring peptide energy landscapes: a test of force fields and implicit solvent models

A biased Monte Carlo-minimization/annealing conformational search was used to characterize five descriptions of the energy landscape for each of three model systems: the 20-residue "trp-cage" miniprotein, the 20-residue "BS1" peptide, and the 17-residue "U(1-17)T9D" peptide. The EEF1 and SASA energy landscapes were studied as well as those defined by using the GB/ACE implicit water model with one of three protein force fields: CHARMM19, CHARMM22, and CHARMM22/CMAP. The lowest-energy structures of the trp-cage and BS1 peptides found for the EEF1 landscape have main-chain root-mean-square deviations (rmsds) from the respective NMR structures of less than 2 A; for U(1-17)T9D, the deviation is less than 3 A using EEF1. The main-chain rmsd of the minimum-energy trp-cage conformation obtained for the GB/ACE/CHARMM22/CMAP landscape is less than 1 A. However, this energy function strongly favored helical structures for the two peptides shown by NMR to form beta-sheet structures. Brief annealing of the system following main-chain conformational changes was found to enhance the exploration of low-energy states. The thousands of simulations reported here suggest that the prediction of protein structure might be improved by the simultaneous use of a CMAP-like description of the main chain and an EEF1-like description of the solvent.

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.

Helix-coil transition of alanine peptides in water: force field dependence on the folded and unfolded structures

The force fields used in classical modeling studies are semiempirical in nature and rely on their validation by comparison of simulations with experimental data. The all-atom replica-exchange molecular dynamics (REMD) methodology allows us to calculate the thermodynamics of folding/unfolding of peptides and small proteins, and provides a way of evaluating the reliability of force fields. We apply the REMD to obtain equilibrium folding/unfolding thermodynamics of a 21-residue peptide containing only alanine residues in explicit aqueous solution. The thermodynamics of this peptide is modeled with both the OPLS/AA/L and the A94/MOD force fields. We find that the helical content and the values for the helix propagation and nucleation parameters for this alanine peptide are consistent with measurements on similar peptides and with calculations using the modified AMBER force field (A94/MOD). The nature of conformations, both folded and unfolded, that contributes to the helix-coil transition profile, however, is quite different between these two force fields.

Properties of integral membrane protein structures: derivation of an implicit membrane potential

Distributions of each amino acid in the trans-membrane domain were calculated as a function of the membrane normal using all currently available alpha-helical membrane protein structures with resolutions better than 4 A. The results were compared with previous sequence- and structure-based analyses. Calculation of the average hydrophobicity along the membrane normal demonstrated that the protein surface in the membrane domain is in fact much more hydrophobic than the protein core. While hydrophobic residues dominate the membrane domain, the interfacial regions of membrane proteins were found to be abundant in the small residues glycine, alanine, and serine, consistent with previous studies on membrane protein packing. Charged residues displayed nonsymmetric distributions with a preference for the intracellular interface. This effect was more prominent for Arg and Lys resulting in a direct confirmation of the positive inside rule. Potentials of mean force along the membrane normal were derived for each amino acid by fitting Gaussian functions to the residue distributions. The individual potentials agree well with experimental and theoretical considerations. The resulting implicit membrane potential was tested on various membrane proteins as well as single trans-membrane alpha-helices. All membrane proteins were found to be at an energy minimum when correctly inserted into the membrane. For alpha-helices both interfacial (i.e. surface bound) and inserted configurations were found to correspond to energy minima. The results demonstrate that the use of trans-membrane amino acid distributions to derive an implicit membrane representation yields meaningful residue potentials.

Molecular modeling of organic and biomolecular systems using BOSS and MCPRO

An overview is provided of the capabilities for the current versions of the BOSS and MCPRO programs for molecular modeling of organic and biomolecular systems. Recent applications are noted, particularly for QM/MM studies of organic and enzymatic reactions and for protein-ligand binding.

Free energy surfaces of miniproteins with a ββα motif: Replica exchange molecular dynamics simulation with an implicit solvation model

Designed miniproteins with a betabetaalpha motif, such as BBA5, 1FSD, and 1PSV can serve as a benchmark set to test the validity of all-atom force fields with computer simulation, because they contain all the basic structural elements in protein folding. Unfortunately, it was found that the standard all-atom force fields with the generalized Born (GB) implicit solvation model tend to produce distorted free energy surfaces for the betabetaalpha proteins, not only because energetically those proteins need to be described by more balanced weights of the alpha- and beta-strands, but also because the GB implicit solvation model suffers from overestimated salt bridge effects. In an attempt to resolve these problems, we have modified one of the standard all-atom force fields in conjunction with the GB model, such that each native state of the betabetaalpha proteins is in its free energy minimum state with reasonable energy barriers separating local minima. With this modified energy model, the free energy contour map in each protein was constructed from the replica exchange molecular dynamics REMD simulation. The resulting free energy surfaces are significantly improved in comparison with previous simulation results and consistent with general views on small protein folding behaviors with realistic topology and energetics of all three proteins.

Transition State Ensemble for the Folding of B Domain of Protein A: A Comparison of Distributed Molecular Dynamics Simulations with Experiments

Folding pathways of the B domain of staphylococcal protein A have been sampled with a distributed computing approach. Starting from an extended structure, the method employs an index measuring topological similarity to the native structure to selectively sample trajectory branches leading to the native fold. Unperturbed and continuous folding trajectories are drawn on a physics-based atomic potential energy surface with an implicit solvent. The sampled folding trajectories demonstrate a similar sequence of events: the earlier stage involves a partial formation of helix 2 and to a less extent of helix 1 at their N terminals, followed by the hydrophobic collapse between residues F14, I17, and L18 on helix 1 and residues R28, F31, and I32 on helix 2, which results in the rigidification of the helix turn from R28 to I32. Helix 2 is then able to extend, allowing for the formation to turn 2. The above description explains one experimental result why a G30A mutant of the protein was observed to be the fastest folder among proteins of its size. And the ensemble of structures right before the final collapse is in good agreement with the transition state ensemble mapped by another recent experiment with Fersht Phi values. We emphasize that because the approach here does not provide quantifications of the free energy landscape, our model of the transition state ensemble emerges from comparisons of simulations and previous experimental results rather from the simulation results alone. On the other hand, as our approach does not rely on a low-dimensional free energy surface, it can complement methods based on the construction of free energy surfaces.

Theoretical Characterization of α-Helix and β-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 Muñoz et al. [Muñoz 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.

Residual Native Structure in a Thermally Denatured β-Hairpin

We investigate the thermal denaturation of trpzip2 between 15 and 82 degrees C using two-dimensional infrared (2D IR) vibrational spectroscopy, dispersed vibrational echo (DVE) spectroscopy, and Fourier transform infrared (FTIR) spectroscopy. The FTIR and DVE spectra of trpzip2 show in the amide I region of the spectrum two resonances, which arise primarily from the interstrand coupling between local amide I oscillators along the peptide backbone. The coupling is seen directly in the 2D IR spectra as the formation of cross-peak ridges. Although small shifts of these frequencies occur on heating the sample, the existence of cross-peak ridges at all temperatures indicates that stable hydrogen bond interactions persist between the two beta-strands. These observations indicate a significant amount of native structure in the thermally denatured state of trpzip2.

Thermodynamic and kinetic characterization of a β-hairpin peptide in solution: An extended phase space sampling by molecular dynamics simulations in explicit water

The folding of the amyloidogenic H1 peptide MKHMAGAAAAGAVV taken from the syrian hamster prion protein is explored in explicit aqueous solution at 300 K using long time scale all-atom molecular dynamics simulations for a total simulation time of 1.1 mus. The system, initially modeled as an alpha-helix, preferentially adopts a beta-hairpin structure and several unfolding/refolding events are observed, yielding a very short average beta-hairpin folding time of approximately 200 ns. The long time scale accessed by our simulations and the reversibility of the folding allow to properly explore the configurational space of the peptide in solution. The free energy profile, as a function of the principal components (essential eigenvectors) of motion, describing the main conformational transitions, shows the characteristic features of a funneled landscape, with a downhill surface toward the beta-hairpin folded basin. However, the analysis of the peptide thermodynamic stability, reveals that the beta-hairpin in solution is rather unstable. These results are in good agreement with several experimental evidences, according to which the isolated H1 peptide adopts very rapidly in water beta-sheet structure, leading to amyloid fibril precipitates [Nguyen et al., Biochemistry 1995;34:4186-4192; Inouye et al., J Struct Biol 1998;122:247-255]. Moreover, in this article we also characterize the diffusion behavior in conformational space, investigating its relations with folding/unfolding conditions.