Exploring the free energy landscape of a model β‐hairpin peptide and its isoform

Secondary structural transitions from α‐helix to β‐sheet conformations are observed in several misfolding diseases including Alzheimer's and Parkinson's. Determining factors contributing favorably to the formation of each of these secondary structures is therefore essential to better understand these disease states. β‐hairpin peptides form basic components of anti‐parallel β‐sheets and are suitable model systems for characterizing the fundamental forces stabilizing β‐sheets in fibrillar structures. In this study, we explore the free energy landscape of the model β‐hairpin peptide GB1 and its E2 isoform that preferentially adopts α‐helical conformations at ambient conditions. Umbrella sampling simulations using all‐atom models and explicit solvent are performed over a large range of end‐to‐end distances. Our results show the strong preference of GB1 and the E2 isoform for β‐hairpin and α‐helical conformations, respectively, consistent with previous studies. We show that the unfolded states of GB1 are largely populated by misfolded β‐hairpin structures which differ from each other in the position of the β‐turn. We discuss the energetic factors contributing favorably to the formation of α‐helix and β‐hairpin conformations in these peptides and highlight the energetic role of hydrogen bonds and non‐bonded interactions. Proteins 2014; 82:2394–2402. © 2014 Wiley Periodicals, Inc.     

Peptide binding to the PDZ3 domain by conformational selection

The PDZ domains, a large family of peptide recognition proteins, bind to the C‐terminal segment of membrane ion channels and receptors thereby mediating their localization. The peptide binding process is not known in detail and seems to differ among different PDZ domains. For the third PDZ domain of the synaptic protein PSD‐95 (PDZ3), a lock‐and‐key mechanism was postulated on the basis of the almost perfect overlap of the crystal structures in the presence and absence of its peptide ligand. Here, peptide binding to PDZ3 is investigated by explicit solvent molecular dynamics (MD) simulations (for a total of 1.3 μs) and the cut‐based free energy profile method for determining free energy barriers and basins. The free energy landscape of apo PDZ3 indicates that there are multiple basins within the native state. These basins differ by the relative orientation of the α2 helix and β2 strand, the two secondary structure elements that make up the peptide binding site. Only the structure with the smallest aperture of the binding site is populated in the MD simulations of the complex whose analysis reveals that the peptide ligand binds to PDZ3 by selecting one of three conformations. Thus, the dynamical information obtained by the atomistic simulations increment the static, that is, partial, picture of the PDZ3 binding mechanism based on the X‐ray crystallography data. Importantly, the simulation results show for the first time that conformational selection is a possible mechanism of peptide binding by PDZ domains in general. Proteins 2012. © 2012 Wiley Periodicals, Inc.     

Explicit and implicit water simulations of a beta-hairpin peptide.

The conformational properties of a beta-hairpin peptide (YITNSDGTWT) were studied by using both explicit and implicit water simulations. The conformational space of the peptide was scanned by using a restricted hydrogen-bonding search method. The search method used generated the conformational space with enough diversity and good representation of beta-hairpin structures. By using a total surface area-based treatment of hydrophobic interactions, implicit water simulations failed to discriminate between experimental beta-hairpin structures from the rest of the conformers present in the authors' conformation library. However, with inclusion of vibrational free energy and accounting separately for polar and nonpolar surface areas, the nuclear magnetic resonance structure was ranked successfully as the most stable conformation. There is a loose correlation between the conformational energies by the continuum model and the conformational energies by explicit water simulation for conformers with similar structures. However, in terms of solvation energy, both approaches have a much better correlation. By using proper treatment of surface effect (partition of the surface area into polar and nonpolar areas) and including vibrational free-energy contribution, the continuum models should be reliable. Furthermore, the authors found that, for this peptide, beta-hairpin structures have large vibrational entropy that contributes decisively to the stability of folded beta-hairpin structures. Proteins 1999;37:73-87.     

A comparison of the different helices adopted by ��- and ��-peptides suggests different reasons for their stability

The right‐handed α‐helix is the dominant helical fold of α‐peptides, whereas the left‐handed 3₁₄‐helix is the dominant helical fold of β‐peptides. Using molecular dynamics simulations, the properties of α‐helical α‐peptides and 3₁₄‐helical β‐peptides with different C‐terminal protonation states and in the solvents water and methanol are compared. The observed energetic and entropic differences can be traced to differences in the polarity of the solvent‐accessible surface area and, in particular, the solute dipole moments, suggesting different reasons for their stability.     

Linear response theory: An alternative to PB and GB methods for the analysis of molecular dynamics trajectories?

We explore the use of classical Linear Response Theory (LRT) as an alternative strategy to the use of Molecular Mechanics/Poisson-Boltzmann strategies to compute the solvation free energy of macromolecules from molecular dynamics simulations using an explicit representation of solvent. The method reproduces well the free energy of solvation of standard amino acid side chains, small peptides, and proteins. The use of a fully discrete representation of solvent avoids the possible problems of continuum models to represent the solvation of systems containing tightly bound water molecules.     

Molecules‐in‐molecules fragment‐based method for the calculation of chiroptical spectra of large molecules: Vibrational circular dichroism and Raman optical activity spectra of alanine polypeptides

The molecules‐in‐molecules (MIM) fragment‐based method has recently been adapted to evaluate the chiroptical (vibrational circular dichroism [VCD] and Raman optical activity [ROA]) spectra of large molecules such as peptides. In the MIM‐VCD and MIM‐ROA methods, the relevant higher energy derivatives of the parent molecule are assembled from the corresponding derivatives of smaller fragment subsystems. In addition, the missing long‐range interfragment interactions are accounted at a computationally less expensive level of theory (MIM2). In this work we employed the MIM‐VCD and MIM‐ROA fragment‐based methods to explore the evolution of the chiroptical spectroscopic characteristics of 3₁₀‐helix, α‐helix, β‐hairpin, γ‐turn, and β‐extended conformers of gas phase polyalanine (chain length n = 6–14). The different conformers of polyalanine show distinctive features in the MIM chiroptical spectra and the associated spectral intensities increase with evolution of system size. For a better understanding the site‐specific effects on the vibrational spectra, isotopic substitutions were also performed employing the MIM method. An increasing redshift with the number of isotopically labeled ¹³C=O functional groups in the peptide molecule was seen. For larger polypeptides, we implemented the two‐step‐MIM model to circumvent the high computational expense associated with the evaluation of chiroptical spectra at a high level of theory using large basis sets. The chiroptical spectra of α‐(alanine)₂₀ polypeptide obtained using the two‐step‐MIM model, including continuum solvation effects, show good agreement with the full calculations and experiment. This benchmark study suggests that the MIM‐fragment approach can assist in predicting and interpreting chiroptical spectra of large polypeptides.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.     

Building a foundation for structure‐based cellulosome design for cellulosic ethanol: Insight into cohesin‐dockerin complexation from computer simulation

The organization and assembly of the cellulosome, an extracellular multienzyme complex produced by anaerobic bacteria, is mediated by the high‐affinity interaction of cohesin domains from scaffolding proteins with dockerins of cellulosomal enzymes. We have performed molecular dynamics simulations and free energy calculations on both the wild type (WT) and D39N mutant of the C. thermocellum Type I cohesin‐dockerin complex in aqueous solution. The D39N mutation has been experimentally demonstrated to disrupt cohesin‐dockerin binding. The present MD simulations indicate that the substitution triggers significant protein flexibility and causes a major change of the hydrogen‐bonding network in the recognition strips—the conserved loop regions previously proposed to be involved in binding—through electrostatic and salt‐bridge interactions between β‐strands 3 and 5 of the cohesin and α‐helix 3 of the dockerin. The mutation‐induced subtle disturbance in the local hydrogen‐bond network is accompanied by conformational rearrangements of the protein side chains and bound water molecules. Additional free energy perturbation calculations of the D39N mutation provide differences in the cohesin‐dockerin binding energy, thus offering a direct, quantitative comparison with experiments. The underlying molecular mechanism of cohesin‐dockerin complexation is further investigated through the free energy profile, that is, potential of mean force (PMF) calculations of WT cohesin‐dockerin complex. The PMF shows a high‐free energy barrier against the dissociation and reveals a stepwise pattern involving both the central β‐sheet interface and its adjacent solvent‐exposed loop/turn regions clustered at both ends of the β‐barrel structure.     

Conformational analysis of endothelin-1: Effects of solvation free energy

In order to investigate conformational preferences of the 21-residue peptide hormone endothelin-1 (ET-1), an extensive conformational search was carried out in vacuo using a combination of high temperature molecular dynamics / annealing and a Monte Carlo / minimization search in torsion angle space. Fully minimized conformations from the search were grouped into families using a clustering technique based on rms fitting over the Cartesian coordinates of the atoms of the peptide backbone of the ring region. A wide range of local energy minima were identified even though two disulfide bridges (Cys¹-Cys¹⁵ and Cys³-Cys¹¹) constrain the structure of the peptide. Low energy conformers of ET-1 as a nonionized species in vacuo arestabilized by intramolecular interaction of the ring region (residues 1-15) with the tail (residues 16–21). Strained conformations for individual residues are observed. Conformational similarity to protein loops is established by matching to protein crystal structures In order to assess the influence of aqueous environment on conformational preference, the electrostatic contribution to the solvation energy was calculated for ET-1 as a fully ionized species (Asp⁸, Lys⁹, Glu¹⁰, Asp¹⁸, N- and C-terminus) using a continuum electrostatics model (DelPhi) for each of the conformed generated in vacuo, and the total solvation free energy was estimated by adding a hydrophobic contribution proportional to solvent accessible surface area. Solvation dramatically alters the relative energetics of ET-1 conformers from that calculated in vacuo. Conformers of ET-1 favored by the electrostatic salvation energy in water include conformers with helical secondary structure in the region of residues 9–15. Perhaps of most importance, it was demonstrated that the contribution tosolvation by an individual charge depends not only on its solvent accessibility but on the proximity of other charges, i.e., it is a cooperative effect. This was shown by the calculation of electrostatic solvation energy as afunction of conformation with individual charges systematically turned “on” and “off”. The cooperative effect of multiple charges on solvation demonstrated in this manner calls into question models that relate solvation energysimply to solvent accessibility by atom or residue alone. © 1995 John Wiley & Sons, Inc.     

An Effective Solvation Term Based on Atomic Occupancies for Use in Protein Simulations

Abstract

Several approaches to the treatment of solvent effects based on continuum models are reviewed and a new method based on occupied atomic volumes (occupancies) is proposed and tested. The new method describes protein-water interactions in terms of atomic solvation parameters, which represent the solvation free energy per unit of volume. These parameters were determined for six different atoms types, using experimental free energies of solvation. The method was implemented in the GROMOS and PRESTO molecular simulation program suites. Simulations with the solvation term require 20-50% more CPU time than the corresponding vacuum simulations and are approximately 20 times faster than explicit water simulations. The method and parameters were tested by carrying out 200 ps simulations of BPTI in water, in vacuo, and with the solvation term. The performance of the solvation term was assessed by comparing the structures and energies from the solvation simulations with the equivalent quantities derived from several BPTI crystal structures and from the explicit water and vacuum simulations. The model structures were evaluated in terms of exposed total surface, buried and exposed polar surfaces, secondary structure preservation, number of hydrogen bonds, energy contributions, and positional deviations from BPTI crystal structures. Vacuum simulations produced unrealistic structures with respect to all criteria applied. The structures resulting from the simulations with explicit water were closer to the 5PTI crystal structure, although part of the secondary structure dissolved. The simulations with the effective solvation term produce structures that are normal according to all evaluations and in most respects are remarkably similar to the 5PTI crystal structure despite considerable positional fluctuations during the simulations. The segments where the model and crystal structures differ are known to be flexible and the observed difference may be physically realistic. The effective solvation term based on occupancies is not only very efficient in terms of computer time but also results in meaningful structural properties for BPTI. It may therefore be generally useful in molecular dynamics of macromolecules.     

The stability of cylindrin β‐barrel amyloid oligomer models—A molecular dynamics study

Small‐soluble amyloid oligomers are believed to play a significant role in the pathology of amyloid diseases. Recently, the atomic structure of a toxic oligomer formed by an 11 residue and its tandem repeat was found to have an out‐off register antiparallel β‐strands in the shape of a β‐barrel. In the present article we investigate the effect of mutations in the hydrophobic cores on the structure and dynamic of the β‐barrels using all atom multiple molecular dynamics simulations with an explicit solvent. Extending previous experiments with molecular dynamics simulations we systematically test how stability and formation of cylindrin depends on the interplay between hydrophobicity and steric effects of the core residues. We find that strong hydrophobic interactions between geometrically fitting residues keep the strands (both in register and out‐off‐register interface) in close proximity, which in turn stabilizes the side‐chain and main‐chain hydrogen bonds, and the salt bridges on the outer surface along the weak out‐of‐register interface. Our simulations also indicate presence of water molecules in the hydrophobic interior of the cylindrin β‐barrel.Proteins 2013. © 2013 Wiley Periodicals, Inc.     

A simple model for polyproline II structure in unfolded states of alanine-based peptides

The striking similarity between observed circular dichroism spectra of nonprolyl homopolymers and that of regular left-handed polyproline II (P_II) helices prompted Tiffany and Krimm to propose in 1968 that unordered peptides and unfolded proteins are built of P_II segments linked by sharp bends. A large body of experimental evidence, accumulated over the past three decades, provides compelling evidence in support of the original hypothesis of Tiffany and Krimm. Of particular interest are the recent experiments of Shi et al. who find significant P_II structure in a short unfolded alanine-based peptide. What is the physical basis for P_II helices in peptide and protein unfolded states? The widely accepted view is that favorable chain-solvent hydrogen bonds lead to a preference for dynamical fluctuations about noncooperative P_II helices in water. Is this preference simply a consequence of hydrogen bonding or is it a manifestation of a more general trend for unfolded states which are appropriately viewed as chains in a good solvent? The prevalence of closely packed interiors in folded proteins suggests that under conditions that favor folding, water—which is a better solvent for itself than for any polypeptide chain—expels the chain from its midst, thereby maximizing chain packing. Implicit in this view is a complementary idea: under conditions that favor unfolding, chain-solvent interactions are preferred and in a so-called good solvent, chain packing density is minimized. In this work we show that minimization of chain packing density leads to preferred fluctuations for short polyalanyl chains around canonical, noncooperative P_II-like conformations. Minimization of chain packing is modeled using a purely repulsive soft-core potential between polypeptide atoms. Details of chain-solvent interactions are ignored. Remarkably, the simple model captures the essential physics behind the preference of short unfolded alanine-based peptides for P_II helices. Our results are based on a detailed analysis of the potential energy landscape which determines the system''s structural and thermodynamic preferences. We use the inherent structure formalism of Stillinger and Weber, according to which the energy landscape is partitioned into basins of attraction around local minima. We find that the landscape for the experimentally studied seven-residue alanine-based peptide is dominated by fluctuations about two noncooperative structures: the left-handed polyproline II helix and its symmetry mate.     

Zinc binding promotes greater hydrophobicity in Alzheimer's Aβ42 peptide than copper binding: Molecular dynamics and solvation thermodynamics studies

The aggregation of Aβ42 peptides is considered as one of the main causes for the development of Alzheimer's disease. In this context, Zn²⁺ and Cu²⁺ play a significant role in regulating the aggregation mechanism, due to changes in the structural and the solvation free energy of Aβ42. In practice, experimental studies are not able to determine the latter properties, since the Aβ42–Zn²⁺ and Aβ42–Cu²⁺ peptide complexes are intrinsically disordered, exhibiting rapid conformational changes in the aqueous environment. Here, we investigate atomic structural variations and the solvation thermodynamics of Aβ42_, Aβ42–Cu²⁺, and Aβ42–Zn²⁺ systems in explicit solvent (water) by using quantum chemical structures as templates for a metal binding site and combining extensive all-atom molecular dynamics (MD) simulations with a thorough solvation thermodynamic analysis. Our results show that the zinc and copper coordination results in a significant decrease of the solvation free energy in the C-terminal region (Met35-Val40), which in turn leads to a higher structural disorder. In contrast, the β-sheet formation at the same C-terminal region indicates a higher solvation free energy in the case of Aβ42_. The solvation free energy of Aβ42 increases upon Zn²⁺ binding, due to the higher tendency of forming the β-sheet structure at the Leu17-Ala42 residues, in contrast to the case of binding with Cu²⁺. Finally, we find the hydrophobicity of Aβ42–Zn²⁺ in water is greater than in the case of Aβ42–Cu²⁺.     

Intrinsic pKas of ionizable residues in proteins: An explicit solvent calculation for lysozyme

Molecular dynamics simulations of triclinic hen egg white lysozyme in aqueous solution were performed to calculate the intrinsic pK_as of 14 ionizable residues. An all-atom model was used for both solvent and solute, and a single 180 ps simulation in conjunction with a Gaussian fluctuation analysis method was used. An advantage of the Gaussian fluctuation method is that it only requires a single simulation of the system in a reference state to calculate all the pK_as in the protein, in contrast to multiple simulations for the free energy perturbation method. pK_int shifts with respect to reference titratable residues were evaluated and compared to results obtained using a finite difference Poisson-Boltzmann (FDPB) method with a continuum solvent model; overall agreement with the direction of the shifts was generally observed, though the magnitude of the shifts was typically larger with the explicit solvent model. The contribution of the first solvation shell to the total charging free energies of the titratable groups was explicitly evaluated and found to be significant. Dielectric shielding between pairs of titratable groups was examined and found to be smaller than expected. The effect of the approximations used to treat the long-range interactions on the pK_int shifts is discussed. © 1994 Wiley-Liss, Inc.     

Temperature and pressure denaturation of chignolin: Folding and unfolding simulation by multibaric-multithermal molecular dynamics method

A multibaric‐multithermal molecular dynamics (MD) simulation of a 10‐residue protein, chignolin, was performed. All‐atom model with the Amber parm99SB force field was used for the protein and the TIP3P model was used for the explicit water molecules. This MD simulation covered wide ranges of temperature between 260 and 560 K and pressure between 0.1 and 600 MPa and sampled many conformations without getting trapped in local‐minimum free‐energy states. Folding events to the native β‐hairpin structure occurred five times and unfolding events were observed four times. As the temperature and/or pressure increases, fraction of folded chignolin decreases. The partial molar enthalpy change ΔH and partial molar volume change ΔV of unfolding were calculated as ΔH = 24.1 ± 4.9 kJ/mol and ΔV = ?5.6 ± 1.5 cm³/mol, respectively. These values agree well with recent experimental results. Illustrating typical local‐minimum free‐energy conformations, folding and unfolding pathways were revealed. When chignolin unfolds from the β‐hairpin structure, only the C terminus or both C and N termini open first. It may undergo an α‐helix or 3₁₀‐helix structure and finally unfolds to the extended structure. Difference of the mechanism between temperature denaturation and pressure denaturation is also discussed. Temperature denaturation is caused by making the protein transferred to a higher entropy state and making it move around more with larger space. The reason for pressure denaturation is that water molecules approach the hydrophobic residues, which are not well hydrated at the folded state, and some hydrophobic contacts are broken. Proteins 2012;. © 2012 Wiley Periodicals, Inc.     

Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)_n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)_n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.     

Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)_n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)_n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.