Thermodynamics of the alpha-helix-coil transition of amphipathic peptides in a membrane environment: implications for the peptide-membrane binding equilibrium

Amphipathic alpha-helices are the membrane binding motif in many proteins. The corresponding peptides are often random coil in solution but are folded into an alpha-helix upon interaction with the membrane. The energetics of this ubiquitous folding process are still a matter of conjecture. Here, we present a new method to quantitatively analyze the thermodynamics of peptide folding at the membrane interface. We have systematically varied the helix content of a given amphipathic peptide when bound to the membrane and have correlated the thermodynamic binding parameters determined by isothermal titration calorimetry with the alpha-helix content obtained by circular dichroism spectroscopy. The peptides investigated were the antibiotic magainin 2 amide and three analogs in which two adjacent amino acid residues were substituted by their d-enantiomers. The thermodynamic parameters controlling the alpha-helix formation were found to be linearly related to the helicity of the membrane-bound peptides. Helix formation at the membrane surface is characterized by an enthalpy change of DeltaH(helix) approximately -0.7 kcal/mol per residue, an entropy change of DeltaS(helix) approximately -1.9 cal/molK residue and a free energy change of DeltaG(helix)=-0.14 kcal/mol residue. Helix formation is a strong driving force of peptide insertion into the membrane and accounts for about 50 % of the free energy of binding. An increase in temperature entails an unfolding of the membrane-bound helix. The temperature dependence can be described with the Zimm-Bragg theory and the enthalpy of unfolding agrees with that deduced from isothermal titration calorimetry.     

Folding thermodynamics of β‐hairpins studied by replica‐exchange molecular dynamics simulations

We study the differences in folding stability of β‐hairpin peptides, including GB1 hairpin and a point mutant GB1 K10G, as well as tryptophan zippers (TrpZips): TrpZip1, TrpZip2, TrpZip3‐1, and TrpZip4. By performing replica‐exchange molecular dynamics simulations with Amber03* force field (a modified version of Amber ff03) in explicit solvent, we observe ab initio folding of all the peptides except TrpZip3‐1, which is experimentally known to be the least stable among the peptides studied here. By calculating the free energies of unfolding of the peptides at room temperature and folding midpoint temperatures for thermal unfolding of peptides, we find that TrpZip4 and GB1 K10G peptides are the most stable β‐hairpins followed by TrpZip1, GB1, and TrpZip2 in the given order. Hence, the proposed K10G mutation of GB1 peptide results in enhanced stability compared to wild‐type GB1. An important goal of our study is to test whether simulations with Amber 03* model can reproduce experimentally predicted folding stability differences between these peptides. While the stabilities of GB1 and TrpZip1 yield close agreement with experiment, TrpZip2 is found to be less stable than predicted by experiment. However, as heterogenous folding of TrpZip2 may yield divergent thermodynamic parameters by different spectroscopic methods, mismatching of results with previous experimental values are not conclusive of model shortcomings. For most of the cases, molecular simulations with Amber03* can successfully reproduce experimentally known differences between the mutated peptides, further highlighting the predictive capabilities of current state‐of‐the‐art all‐atom protein force fields. Proteins 2015; 83:1307–1315. © 2015 Wiley Periodicals, Inc.     

Structure and energy landscape of a photoswitchable peptide: a replica exchange molecular dynamics study

A replica exchange molecular dynamics (REMD) simulation of a bicyclic azobenzene peptide in explicit dimethyl sulfoxide solution is presented in order to characterize the conformational structures and energy landscape of a photoswitchable peptide. It is shown that an enhanced-sampling technique such as the REMD method is essential to obtain a converged conformational sampling of the peptide at room temperature. This is because conventional MD simulations of less than approximately 100-ns length are either trapped in local minima (at 295 K) or-if run at high temperature-do not resemble the room-temperature REMD results. Calculating various nuclear Overhauser effects (NOEs) and (3)J-couplings, a good overall agreement between the REMD simulations and the NMR experiments of Renner et al. (Biopolymers 2000;54:501-514) is found. In particular, the REMD study confirms the general picture drawn by Renner et al. that the trans-isomer of the azobenzene peptide exhibits a well-defined structure, while the cis-isomer is a conformational heterogeneous system; that is, the trans-isomer occurs in 2 well-defined conformers, while the cis-isomer represents an energetically frustrated system that leads to an ensemble of conformational structures. Employing a principal component analysis of the REMD data, the free energy landscape of the systems is studied at various temperatures. The implications for the folding and unfolding pathways of the system are discussed.     

Unfolding of class A amphipathic peptides on a lipid surface

The folding of polypeptides associated with biomembranes is a ubiquitous phenomenon, yet the thermodynamics underlying the process are poorly understood. In the present work we examine the unfolding of a series of alpha-helical amphipathic membrane-associated peptides using guanidine hydrochloride as a denaturant. The peptides are based on the class A amphipathic helix motif, and each contains a single tryptophan at sequence position 2, 3, 7, 12, or 14. The isothermal unfolding process was monitored by circular dichroism ellipticity at 222 nm to monitor changes in the helical structure of the peptide. Tryptophan fluorescence was used to probe the local changes in the environment about the indole fluorophore. The unfolding curves generated from the two experimental techniques for each peptide-lipid complex were non-coincidental, suggesting the presence of stable intermediate(s) in the unfolding. A three-state model could adequately account for the data and yielded parameters which were consistent with the presence of a partially folded intermediate structure which (i) is closer in Gibb's free energy to the folded state than the unfolded state and (ii) retains much of the interfacial and amphipathic character of the folded state. Denaturant-induced peptide dissociation from the peptide-lipid complexes was found to be negligible as confirmed by size exclusion chromatography. The results are compared with related thermodynamic data and discussed in terms of current models of peptide folding at membrane interfaces.     

Helix nucleation kinetics from molecular simulations in explicit solvent

We study the reversible folding/unfolding of short Ala and Gly-based peptides by molecular dynamics simulations of all-atom models in explicit water solvent. A kinetic analysis shows that the formation of a first alpha-helical turn occurs within 0.1-1 ns, in agreement with the analyses of laser temperature jump experiments. The unfolding times exhibit Arrhenius temperature dependence. For a rapidly nucleating all-Ala peptide, the helix nucleation time depends only weakly on temperature. For a peptide with enthalpically competing turn-like structures, helix nucleation exhibits an Arrhenius temperature dependence, corresponding to the unfolding of enthalpic traps in the coil ensemble. An analysis of structures in a "transition-state ensemble" shows that helix-to-coil transitions occur predominantly through breaking of hydrogen bonds at the helix ends, particularly at the C-terminus. The temperature dependence of the transition-state ensemble and the corresponding folding/unfolding pathways illustrate that folding mechanisms can change with temperature, possibly complicating the interpretation of high-temperature unfolding simulations. The timescale of helix formation is an essential factor in molecular models of protein folding. The rapid helix nucleation observed here suggests that transient helices form early in the folding event.     

Secondary Structure Propensities in Peptide Folding Simulations: A Systematic Comparison of Molecular Mechanics Interaction Schemes

We present a systematic study directed toward the secondary structure propensity and sampling behavior in peptide folding simulations with eight different molecular dynamics force-field variants in explicit solvent. We report on the combinational result of force field, water model, and electrostatic interaction schemes and compare to available experimental characterization of five studied model peptides in terms of reproduced structure and dynamics. The total simulation time exceeded 18 μs and included simulations that started from both folded and extended conformations. Despite remaining sampling issues, a number of distinct trends in the folding behavior of the peptides emerged. Pronounced differences in the propensity of finding prominent secondary structure motifs in the different applied force fields suggest that problems point in particular to the balance of the relative stabilities of helical and extended conformations.     

The investigation of the secondary structure propensities and free-energy landscapes of peptide ligands by replica exchange molecular dynamics simulations

The conformational states of two peptide sequences that bind to staphylococcal enterotoxin B are sampled by replica exchange molecular dynamic (REMD) simulations in explicit water. REMD simulations were treated with 52 replicas in the range of 280–501 K for both peptides. The conformational ensembles of both peptides are dominated by random coil, bend and turn structures with a small amount of helical structures for each temperature. In addition, while an insignificant presence of β-bridge structures were observed for both peptides, the β-sheet structure was observed only for peptide 3. The results obtained from simulations at 300 K are consistent with the experimental results obtained from circular dichroism spectroscopy. From the analysis of REMD results, we also calculated hydrophobic and hydrophilic solvent accessible surface areas for both peptides, and it was observed that the hydrophobic segments of the peptides tend to form bend or turn structures. Moreover, the free-energy landscapes of both peptides were obtained by principal component analysis to understand how the secondary structural properties change according to their complex space. From the free-energy analysis, we have found several minima for both peptides at decreased temperature. For these obvious minima of both peptides, it was observed that the random coil, bend and turn structures are still dominant and the helix, β-bridge or β-sheet structures can appear or disappear with respect to minima. On the other hand, when we compare the results of REMD with conventional MD simulations for these peptides, the configurations of peptide 3 might be trapped in energy minima during the conventional MD simulations. Hence, it can be said that the REMD simulations have provided a sufficiently high sampling efficiency.     

The triplex-hairpin transition in cytosine-rich DNA

We present a theoretical study of the self-complementary single-stranded 30-mer d(TC*TTC*C*TTTTCCTTCTC*CCGAGAAGGTTTT) (PDB ID: 1b4y) that was designed to form an intramolecular triplex by folding back twice on itself. At neutral pH the molecule exists in a duplex hairpin conformation, whereas at acidic pH the cytosines labeled by an asterisk (*) are protonated, forming Hoogsteen hydrogen bonds with guanine of a GC Watson-Crick basepair to generate a triplex. As a first step in an investigation of the energetics of the triplex-hairpin transition, we applied the Bashford-Karplus multiple site model of protonation to calculate the titration curves for the two conformations. Based on these data, a two-state model is used to study the equilibrium properties of transition. Although this model properly describes the thermodynamics of the protonation-deprotonation steps that drive the folding-unfolding of the oligomer, it cannot provide insight into the time-dependent mechanism of the process. A series of molecular dynamics simulations using the ff94 force field of the AMBER 6.0 package was therefore run to explore the dynamics of the folding/unfolding pathway. The molecular dynamics method was combined with Poisson-Boltzmann calculations to determine when a change in protonation state was warranted during a trajectory. This revealed a sequence of elementary protonation steps during the folding/unfolding transition and suggests a strong coupling between ionization and folding in cytosine-rich triple-helical triplexes.     

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.     

An Analysis of Biomolecular Force Fields for Simulations of Polyglutamine in Solution

Polyglutamine (polyQ) peptides are a useful model system for biophysical studies of protein folding and aggregation, both for their intriguing aggregation properties and their own relevance to human disease. The genetic expansion of a polyQ tract triggers the formation of amyloid aggregates associated with nine neurodegenerative diseases. Several clearly identifiable and separable factors, notably the length of the polyQ tract, influence the mechanism of aggregation, its associated kinetics, and the ensemble of structures formed. Atomistic simulations are well positioned to answer open questions regarding the thermodynamics and kinetics of polyQ folding and aggregation. The additional, explicit representation of water permits deeper investigation of the role of solvent dynamics, and it permits a direct comparison of simulation results with infrared spectroscopy experiments. The generation of meaningful simulation results hinges on satisfying two essential criteria: achieving sufficient conformational sampling to draw statistically valid conclusions, and accurately reproducing the intermolecular forces that govern system structure and dynamics. In this work, we examine the ability of 12 biomolecular force fields to reproduce the properties of a simple, 30-residue polyQ peptide (Q₃₀) in explicit water. In addition to secondary and tertiary structure, we consider generic structural properties of polymers that provide additional dimensions for analysis of the highly degenerate disordered states of the molecule. We find that the 12 force fields produce a wide range of predictions. We identify AMBER ff99SB, AMBER ff99SB^∗, and OPLS-AA/L to be most suitable for studies of polyQ folding and aggregation.     

Microsecond simulations of the folding/unfolding thermodynamics of the Trp‐cage miniprotein

We study the unbiased folding/unfolding thermodynamics of the Trp‐cage miniprotein using detailed molecular dynamics simulations of an all‐atom model of the protein in explicit solvent using the Amberff99SB force field. Replica‐exchange molecular dynamics simulations are used to sample the protein ensembles over a broad range of temperatures covering the folded and unfolded states at two densities. The obtained ensembles are shown to reach equilibrium in the 1 μs/replica timescale. The total simulation time used in the calculations exceeds 100 μs. Ensemble averages of the fraction folded, pressure, and energy differences between the folded and unfolded states as a function of temperature are used to model the free energy of the folding transition, ΔG(P, T), over the whole region of temperatures and pressures sampled in the simulations. The ΔG(P, T) diagram describes an ellipse over the range of temperatures and pressures sampled, predicting that the system can undergo pressure‐induced unfolding and cold denaturation at low temperatures and high pressures, and unfolding at low pressures and high temperatures. The calculated free energy function exhibits remarkably good agreement with the experimental folding transition temperature (T_f = 321 K), free energy, and specific heat changes. However, changes in enthalpy and entropy are significantly different than the experimental values. We speculate that these differences may be due to the simplicity of the semiempirical force field used in the simulations and that more elaborate force fields may be required to describe appropriately the thermodynamics of proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Gain of local structure in an amphipathic peptide does not require a specific tertiary framework

In this work, we studied how an amphipathic peptide of the surface of the globular protein thioredoxin, TRX94‐108, acquires a native‐like structure when it becomes involved in an apolar interaction network. We designed peptide variants where the tendency to form α‐helical conformation is modulated by replacing each of the leucine amino acid residues by an alanine. The induction of structure caused by sodium dodecyl sulfate (SDS) binding was studied by capillary zone electrophoresis, circular dichroism, DOSY‐NMR, and molecular dynamics simulations (MDS). In addition, we analyzed the strength of the interaction between a C18 RP‐HPLC matrix and the peptides. The results presented here reveal that (a) critical elements in the sequence of the wild‐type peptide stabilize a SDS/peptide supramolecular cluster; (b) the hydrophobic nature of the interaction between SDS molecules and the peptide constrains the ensemble of conformations; (c) nonspecific apolar surfaces are sufficient to stabilize peptide secondary structure. Remarkably, MDS shed light on a contact network formed by a limited number of SDS molecules that serves as a structural scaffold preserving the helical conformation of this module. This mechanism might prevail when a peptide with low helical propensity is involved in structure consolidation. We suggest that folding of peptides sharing this feature does not require a preformed tightly‐packed protein core. Thus, the formation of specific tertiary interactions would be the consequence of peptide folding and not its cause. In this scenario, folding might be thought of as a process that includes unspecific rounds of structure stabilization guiding the protein to the native state. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Computational investigation of the effect of thermal perturbation on the mechanical unfolding of titin I27

The emergence of single-molecule force measurement experiments has facilitated a better understanding of protein folding pathways and the thermodynamics involved. Computational methods such as steered molecular dynamics (SMD) simulations are helpful in providing atomistic level information on the unfolding pathways. Recent experimental studies have showed that combinations of single-molecule experiments with traditional methods such as chemical and/or thermal denaturation yield additional insights into the folding phenomenon. In this study, we report results from extensive computations (a total of about 60 SMD simulations with a total length of about 0.4 μs) that address the effect of thermal perturbation on the mechanical stability of the I27 domain of the protein titin. A wide range of temperatures (280-340 K) were considered for the pulling, which was done at both constant velocity and constant force using SMD simulations. Good agreement with experimental data, such as for the trends in changes in average force and the maximum force with respect to the temperature, was obtained. This study identifies two competing pathways for the mechanical unfolding of I27, and illustrates the significance of combining various techniques to examine protein folding.     

Computer simulations of protein folding by targeted molecular dynamics

We have performed 128 folding and 45 unfolding molecular dynamics runs of chymotrypsin inhibitor 2 (CI2) with an implicit solvation model for a total simulation time of 0.4 microseconds. Folding requires that the three-dimensional structure of the native state is known. It was simulated at 300 K by supplementing the force field with a harmonic restraint which acts on the root-mean-square deviation and allows to decrease the distance to the target conformation. High temperature and/or the harmonic restraint were used to induce unfolding. Of the 62 folding simulations started from random conformations, 31 reached the native structure, while the success rate was 83% for the 66 trajectories which began from conformations unfolded by high-temperature dynamics. A funnel-like energy landscape is observed for unfolding at 475 K, while the unfolding runs at 300 K and 375 K as well as most of the folding trajectories have an almost flat energy landscape for conformations with less than about 50% of native contacts formed. The sequence of events, i.e., secondary and tertiary structure formation, is similar in all folding and unfolding simulations, despite the diversity of the pathways. Previous unfolding simulations of CI2 performed with different force fields showed a similar sequence of events. These results suggest that the topology of the native state plays an important role in the folding process.     

Evaluation of a fast implicit solvent model for molecular dynamics simulations.

A solvation term based on the solvent accessible surface area (SASA) is combined with the CHARMM polar hydrogen force field for the efficient simulation of peptides and small proteins in aqueous solution. Only two atomic solvation parameters are used: one is negative for favoring the direct solvation of polar groups and the other positive for taking into account the hydrophobic effect on apolar groups. To approximate the water screening effects on the intrasolute electrostatic interactions, a distance-dependent dielectric function is used and ionic side chains are neutralized. The use of an analytical approximation of the SASA renders the model extremely efficient (i.e., only about 50% slower than in vacuo simulations). The limitations and range of applicability of the SASA model are assessed by simulations of proteins and structured peptides. For the latter, the present study and results reported elsewhere show that with the SASA model it is possible to sample a significant amount of folding/unfolding transitions, which permit the study of the thermodynamics and kinetics of folding at an atomic level of detail.     

Reproducible polypeptide folding and structure prediction using molecular dynamics simulations

The folding of a polypeptide from an extended state to a well-defined conformation is studied using microsecond classical molecular dynamics (MD) simulations and replica exchange molecular dynamics (REMD) simulations in explicit solvent and in vacuo. It is shown that the solvated peptide folds many times in the REMD simulations but only a few times in the conventional simulations. From the folding events in the classical simulations we estimate an approximate folding time of 1-2 micros. The REMD simulations allow enough sampling to deduce a detailed Gibbs free energy landscape in three dimensions. The global minimum of the energy landscape corresponds to the native state of the peptide as determined previously by nuclear magnetic resonance (NMR) experiments. Starting from an extended state it takes about 50 ns before the native structure appears in the REMD simulations, about an order of magnitude faster than conventional MD. The calculated melting curve is in good qualitative agreement with experiment. In vacuo, the peptide collapses rapidly to a conformation that is substantially different from the native state in solvent.     

Folding is not required for bilayer insertion: replica exchange simulations of an alpha-helical peptide with an explicit lipid bilayer

We implement the replica exchange molecular dynamics algorithm to study the interactions of a model peptide (WALP-16) with an explicitly represented DPPC membrane bilayer. We observe the spontaneous, unbiased insertion of WALP-16 into the DPPC bilayer and its folding into an alpha-helix with a transbilayer orientation. The free energy surface suggests that the insertion of the peptide into the DPPC bilayer precedes secondary structure formation. Although the peptide has some propensity to form a partially helical structure in the interfacial region of the DPPC/water system, this state is not a productive intermediate but rather an off-pathway trap for WALP-16 insertion. Equilibrium simulations show that the observed insertion/folding pathway mirrors the potential of mean force (PMF). Calculation of the enthalpic and entropic contributions to this PMF show that the surface bound conformation of WALP-16 is significantly lower in energy than other conformations, and that the insertion of WALP-16 into the bilayer without regular secondary structure is enthalpically unfavorable by 5-10 kcal/mol/residue. The observed insertion/folding pathway disagrees with the dominant conceptual model, which is that a surface-bound helix is an obligatory intermediate for the insertion of alpha-helical peptides into lipid bilayers. In our simulations, the observed insertion/folding pathway is favored because of a large (>100 kcal/mol) increase in system entropy that occurs when the unstructured WALP-16 peptide enters the lipid bilayer interior. The insertion/folding pathway that is lowest in free energy depends sensitively on the near cancellation of large enthalpic and entropic terms. This suggests the possibility that intrinsic membrane peptides may have a diversity of insertion/folding behaviors depending on the exact system of peptide and lipid under consideration.     

Nanosecond temperature jump relaxation dynamics of cyclic beta-hairpin peptides

The thermal unfolding of a series of 6-, 10-, and 14-mer cyclic beta-hairpin peptides was studied to gain insight into the mechanism of formation of this important secondary structure. The thermodynamics of the transition were characterized using temperature dependent Fourier transform infrared spectroscopy. Thermodynamic data were analyzed using a two-state model which indicates increasing cooperativity along the series. The relaxation kinetics of the peptides in response to a laser induced temperature jump were probed using time-resolved infrared spectroscopy. Single exponential relaxation kinetics were observed and fit with a two-state model. The folding rate determined for these cyclic peptides is accelerated by some two orders of magnitude over the rate of a linear peptide that forms a beta-hairpin. This observation supports the argument that the rate limiting step in the linear system is either stabilization of compact collapsed structures or rearrangement of collapsed structures over a barrier to achieve the native interstrand registry. Small activation energies for folding of these peptides obtained from an Arrhenius analysis of the rates imply a primarily entropic barrier, hence an organized transition state having specific stabilizing interactions.     

Three force fields' views of the 3(10) helix

Slowly but steadily bibliographic evidence is accumulating that the apparent convergence of the various biomolecular force fields as evidenced from simulations of proteins in the folded state does not hold true for folding simulations. Here we add one more example to the growing list of peptides and proteins for which different force fields show irreconcilable differences in their folding predictions, even at such a fundamental level as that of a peptide's secondary structure. We show that for an undecamer peptide that is known from two independent NMR structure determinations to have a mainly 3₁₀-helical structure in solution, three mainstream biomolecular force fields give completely disparate predictions: The CHARMM force field (with the CMAP correction) predicts an outstandingly stable α-helical structure, in disagreement not only with the experimental structures, but also with experimental evidence obtained from circular dichroism. OPLS-AA shows an almost totally disordered peptide with the most frequently observed folded conformation corresponding to a β-hairpin-like structure, again in disagreement with all available experimental evidence. Only the AMBER99SB force field appears to qualitatively agree with not only the general structural characteristics of the peptide (on the account of both NMR- and CD-based experiments), but to also correctly predict some of the experimentally observed interactions at the level of side chains. Possible interpretations of these findings are discussed.