Folding simulations of alanine-based peptides with lysine residues.

The folding of short alanine-based peptides with different numbers of lysine residues is simulated at constant temperature (274 K) using the rigid-element Monte Carlo method. The solvent-referenced potential has prevented the multiple-minima problem in helix folding. From various initial structures, the peptides with three lysine residues fold into helix-dominated conformations with the calculated average helicity in the range of 60-80%. The peptide with six lysine residues shows only 8-14% helicity. These results agree well with experimental observations. The intramolecular electrostatic interaction of the charged lysine side chains and their electrostatic hydration destabilize the helical conformations of the peptide with six lysine residues, whereas these effects on the peptides with three lysine residues are small. The simulations provide insight into the helix-folding mechanism, including the beta-bend intermediate in helix initiation, the (i, i + 3) hydrogen bonds, the asymmetrical helix propagation, and the asymmetrical helicities in the N- and C-terminal regions. These findings are consistent with previous studies.     

Essential dynamics of reversible peptide folding: memory-free conformational dynamics governed by internal hydrogen bonds

A principal component analysis has been applied on equilibrium simulations of a beta-heptapeptide that shows reversible folding in a methanol solution. The analysis shows that the configurational space contains only three dense sub-states. These states of relatively low free energy correspond to the "native" left-handed helix, a partly helical intermediate, and a hairpin-like structure. The collection of unfolded conformations form a relatively diffuse cloud with little substructure. Internal hydrogen-bonding energies were found to correlate well with the degree of folding. The native helical structure folds from the N terminus; the transition from the major folding intermediate to the native helical structure involves the formation of the two most C-terminal backbone hydrogen bonds. A four-state Markov model was found to describe transition frequencies between the conformational states within error limits, indicating that memory-effects are negligible beyond the nanosecond time-scale. The dominant native state fluctuations were found to be very similar to unfolding motions, suggesting that unfolding pathways can be inferred from fluctuations in the native state. The low-dimensional essential subspace, describing 69% of the collective atomic fluctuations, was found to converge at time-scales of the order of one nanosecond at all temperatures investigated, whereas folding/unfolding takes place at significantly longer time-scales, even above the melting temperature.     

Conformational features of a hexapeptide model Ac-TGAAKA-NH2 corresponding to a hydrated alpha helical segment from glyceraldehyde 3-phosphate dehydrogenase: implications for the role of turns in helix folding

Recent analysis of alpha helices in protein crystal structures, available in literature, revealed hydrated alpha helical segments in which, water molecule breaks open helix 5-->1 hydrogen bond by inserting itself, hydrogen bonds to both C=O and NH groups of helix hydrogen bond without disrupting the helix hydrogen bond, and hydrogen bonds to either C=O or NH of helix hydrogen bond. These hydrated segments display a variety of turn conformations and are thought to be 'folding intermediates' trapped during folding-unfolding of alpha helices. A role for reverse turns is implicated in the folding of alpha helices. We considered a hexapeptide model Ac-1TGAAKA6-NH2 from glyceraldehyde 3-phosphate dehydrogenase, corresponding to a hydrated helical segment to assess its role in helix folding. The sequence is a site for two 'folding intermediates'. The conformational features of the model peptide have been investigated by 1H 2D NMR techniques and quantum mechanical perturbative configuration interaction over localized orbitals (PCILO) method. Theoretical modeling largely correlates with experimental observations. Based upon the amide proton temperature coefficients, the observed d alpha n(i, i + 1), d alpha n(i, i + 2), dnn(i, i + 1), d beta n(i, i + 1) NOEs and the results from theoretical modeling, we conclude that the residues of the peptide sample alpha helical and neck regions of the Ramachandran phi, psi map with reduced conformational entropy and there is a potential for turn conformations at N and C terminal ends of the peptide. The role of reduced conformational entropy and turn potential in helix formation have been discussed. We conclude that the peptide sequence can serve as a 'folding intermediate' in the helix folding of glyceraldehyde 3-phosphate dehydrogenase.     

Helix folding simulations with various initial conformations.

Using a solvent-referenced energy calculation, a 16-residue peptide with alanine side chains folded into predominantly alpha-helical conformations during constant temperature (274 K) simulations. From different initial conformations, helical conformations were reached and the multiple energy minima did not become a serious problem. Under the same conditions, the simulation did not indiscriminately fold a sequence such as polyglycine into stable helices. Interesting observations from the simulations relate to the folding mechanism. The electrostatic interactions between the successive amides favored extended conformations (or beta strands) and caused energy barriers to helix folding. beta-bends were observed as intermediates during helix nucleation. The helix propagation toward the C-terminus seemed faster than that toward the N-terminus. In helical conformations, hydrogen bond oscillation between the i,i+ 4 and the i,i+3 patterns was observed. The i,i+3 hydrogen bonds occurred more frequently during helix propagation and deformation near both ends of the helical segment.     

Refolding simulations of an isolated fragment of barnase into a native-like β hairpin: Evidence for compactness and hydrogen bonding as concurrent stabilizing factors

Experimental evidence and theoretical models both suggest that protein folding is initiated within specific fragments intermittently adopting conformations close to that found in the protein native structure. These folding initiation sites encompassing short portions of the protein are ideally suited for study in isolation by computational methods aimed at peering into the very early events of folding. We have used Molecular Dynamics (MD) technique to investigate the behavior of an isolated protein fragment formed by residues 85 to 102 of barnase that folds into a β hairpin in the protein native structure. Three independent MD simulations of 1.3 to 1.8 ns starting from unfolded conformations of the peptide portrayed with an all-atom model in water were carried out at gradually decreasing temperature. A detailed analysis of the conformational preferences adopted by this peptide in the course of the simulations is presented. Two of the unfolded peptide conformations fold into a hairpin characterized by native and a larger bulk of nonnative interactions. Both refolding simulations substantiate the close relationship between interstrand compactness and hydrogen bonding network involving backbone atoms. Persistent compactness witnessed by side-chain interactions always occurs concomitantly with the formation of backbone hydrogen bonds. No highly populated conformations generated in a third simulation starting from the remotest unfolded conformer relative to the native structure are observed. However, nonnative long-range and medium-range contacts with the aromatic moiety of Trp94 are spotted, which are in fair agreement with a former nuclear magnetic resonance study of a denaturing solution of an isolated barnase fragment encompassing the β hairpin. All this lends reason to believe that the 85–102 barnase fragment is a strong initiation site for folding. Proteins 29:212–227, 1997. © 1997 Wiley-Liss, Inc.     

Deconvoluting Protein (Un)folding Structural Ensembles Using X-Ray Scattering,Nuclear Magnetic Resonance Spectroscopy and Molecular Dynamics Simulation

The folding and unfolding of protein domains is an apparently cooperative process, but transient intermediates have been detected in some cases. Such (un)folding intermediates are challenging to investigate structurally as they are typically not long-lived and their role in the (un)folding reaction has often been questioned. One of the most well studied (un)folding pathways is that of Drosophila melanogaster Engrailed homeodomain (EnHD): this 61-residue protein forms a three helix bundle in the native state and folds via a helical intermediate. Here we used molecular dynamics simulations to derive sample conformations of EnHD in the native, intermediate, and unfolded states and selected the relevant structural clusters by comparing to small/wide angle X-ray scattering data at four different temperatures. The results are corroborated using residual dipolar couplings determined by NMR spectroscopy. Our results agree well with the previously proposed (un)folding pathway. However, they also suggest that the fully unfolded state is present at a low fraction throughout the investigated temperature interval, and that the (un)folding intermediate is highly populated at the thermal midpoint in line with the view that this intermediate can be regarded to be the denatured state under physiological conditions. Further, the combination of ensemble structural techniques with MD allows for determination of structures and populations of multiple interconverting structures in solution.     

The dominant interaction between peptide and urea is electrostatic in nature: a molecular dynamics simulation study

The conformational equilibrium of a blocked valine peptide in water and aqueous urea solution is studied using molecular dynamics simulations. Pair correlation functions indicate enhanced concentration of urea near the peptide. Stronger hydrogen bonding of urea-peptide compared to water-peptide is observed with preference for helical conformation. The potential of mean force, computed using umbrella sampling, shows only small differences between urea and water solvation that are difficult to quantify. The changes in solvent structure around the peptide are explained by favorable electrostatic interactions (hydrogen bonds) of urea with the peptide backbone. There is no evidence for significant changes in hydrophobic interactions in the two conformations of the peptide in urea solution. Our simulations suggest that urea denatures proteins by preferentially forming hydrogen bonds to the peptide backbone, reducing the barrier for exposing protein residues to the solvent, and reaching the unfolded state.     

The sequence TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase displays structural ambivalence and interconverts between alpha-helical and beta-hairpin conformations mediated by collapsed conformational states.

The peptide TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase adopts a helical conformation in the crystal structure and is a site for two hydrated helical segments, which are thought to be helical folding intermediates. Overlapping sequences of four to five residues from the peptide, sample both helical and strand conformations in known protein structures, which are dissimilar to glyceraldehyde-3-phosphate dehydrogenase suggesting that the peptide may have a structural ambivalence. Molecular dynamics simulations of the peptide sequence performed for a total simulation time of 1.2 micros, starting from the various initial conformations using GROMOS96 force field under NVT conditions, show that the peptide samples a large number of conformational forms with transitions from alpha-helix to beta-hairpin and vice versa. The peptide, therefore, displays a structural ambivalence. The mechanism from alpha-helix to beta-hairpin transition and vice versa reveals that the compact bends and turns conformational forms mediate such conformational transitions. These compact structures including helices and hairpins have similar hydrophobic radius of gyration (Rgh) values suggesting that similar hydrophobic interactions govern these conformational forms. The distribution of conformational energies is Gaussian with helix sampling lowest energy followed by the hairpins and coil. The lowest potential energy of the full helix may enable the peptide to take up helical conformation in the crystal structure of the glyceraldehyde-3-phosphate dehydrogenase, even though the peptide has a preference for hairpin too. The relevance of folding and unfolding events observed in our simulations to hydrophobic collapse model of protein folding are discussed.     

High temperature unfolding simulations of the TRPZ1 peptide

We report high temperature molecular dynamics simulations of the unfolding of the TRPZ1 peptide using an explicit model for the solvent. The system has been simulated for a total of 6 μs with 100-ns minimal continuous stretches of trajectory. The populated states along the simulations are identified by monitoring multiple observables, probing both the structure and the flexibility of the conformations. Several unfolding and refolding transition pathways are sampled and analyzed. The unfolding process of the peptide occurs in two steps because of the accumulation of a metastable on-pathway intermediate state stabilized by two native backbone hydrogen bonds assisted by nonnative hydrophobic interactions between the tryptophan side chains. Analysis of the un/folding kinetics and classical commitment probability calculations on the conformations extracted from the transition pathways show that the rate-limiting step for unfolding is the disruption of the ordered native hydrophobic packing (Trp-zip motif) leading from the native to the intermediate state. But, the speed of the folding process is mainly determined by the transition from the completely unfolded state to the intermediate and specifically by the closure of the hairpin loop driven by formation of two native backbone hydrogen bonds and hydrophobic contacts between tryptophan residues. The temperature dependence of the unfolding time provides an estimate of the unfolding activation enthalpy that is in agreement with experiments. The unfolding time extrapolated to room temperature is in agreement with the experimental data as well, thus providing a further validation to the analysis reported here.     

Breaking non-native hydrophobic clusters is the rate-limiting step in the folding of an alanine-based peptide

The formation mechanism of an alanine-based peptide has been studied by all-atom molecular dynamics simulations with a recently developed all-atom point-charge force field and the Generalize Born continuum solvent model at an effective salt concentration of 0.2M. Thirty-two simulations were conducted. Each simulation was performed for 100 ns. A surprisingly complex folding process was observed. The development of the helical content can be divided into three phases with time constants of 0.06-0.08, 1.4-2.3, and 12-13 ns, respectively. Helices initiate extreme rapidly in the first phase similar to that estimated from explicit solvent simulations. Hydrophobic collapse also takes place in this phase. A folding intermediate state develops in the second phase and is unfolded to allow the peptide to reach the transition state in the third phase. The folding intermediate states are characterized by the two-turn short helices and the transition states are helix-turn-helix motifs-both of which are stabilized by hydrophobic clusters. The equilibrium helical content, calculated by both the main-chain Phi-Psi torsion angles and the main-chain hydrogen bonds, is 64-66%, which is in remarkable agreement with experiments. After corrected for the solvent viscosity effect, an extrapolated folding time of 16-20 ns is obtained that is in qualitative agreement with experiments. Contrary to the prevailing opinion, neither initiation nor growth of the helix is the rate-limiting step. Instead, the rate-limiting step for this peptide is breaking the non-native hydrophobic clusters in order to reach the transition state. The implication to the folding mechanisms of proteins is also discussed.     

Membrane adsorption,folding, insertion and translocation of synthetic trans-membrane peptides

Spontaneous membrane adsorption, folding and insertion of the synthetic WALP16 and KALP16 peptides was studied by computer simulations starting from completely extended conformations. The peptides were simulated using an unmodified all-atom force field in combination with an efficient Monte Carlo sampling algorithm. The membrane is represented implicitly as a hydrophobic zone inside a continuum solvent modelled using the generalized Born theory of solvation. The method was previously parameterized to match insertion energies of hydrophobic side chain analogs into cyclohexane and no parameters were optimized for the present simulations. Both peptides rapidly precipitate out of bulk solution and adsorb to the membrane surface. Interfacial folding into a helical conformation is followed by membrane insertion. Both the peptide conformations and their location in the membrane are strongly temperature dependent. The temperature dependent behaviour can be summarized by fitting to a four-state model, separating the system into folded and unfolded conformers, which are either inserted into the membrane or located at the interfaces. As the temperature is lowered the dominant peptide conformation of the system changes from unfolded surface bound configurations to folded surface bound states. Folded trans-membrane conformers represent the dominant configuration at low temperatures. The analysis allows direct estimates of the free energies of peptide folding and membrane insertion. In the case of WALP the quality of the fit is excellent and the thermodynamic behaviour is in good agreement with expected theoretical consideration. For KALP the fit is more problematic due to the large solvation energies of the charged lysine residues.     

Membrane adsorption, folding, insertion and translocation of synthetic trans-membrane peptides

Spontaneous membrane adsorption, folding and insertion of the synthetic WALP16 and KALP16 peptides was studied by computer simulations starting from completely extended conformations. The peptides were simulated using an unmodified all-atom force field in combination with an efficient Monte Carlo sampling algorithm. The membrane is represented implicitly as a hydrophobic zone inside a continuum solvent modelled using the generalized Born theory of solvation. The method was previously parameterized to match insertion energies of hydrophobic side chain analogs into cyclohexane and no parameters were optimized for the present simulations. Both peptides rapidly precipitate out of bulk solution and adsorb to the membrane surface. Interfacial folding into a helical conformation is followed by membrane insertion. Both the peptide conformations and their location in the membrane are strongly temperature dependent. The temperature dependent behaviour can be summarized by fitting to a four-state model, separating the system into folded and unfolded conformers, which are either inserted into the membrane or located at the interfaces. As the temperature is lowered the dominant peptide conformation of the system changes from unfolded surface bound configurations to folded surface bound states. Folded trans-membrane conformers represent the dominant configuration at low temperatures. The analysis allows direct estimates of the free energies of peptide folding and membrane insertion. In the case of WALP the quality of the fit is excellent and the thermodynamic behaviour is in good agreement with expected theoretical consideration. For KALP the fit is more problematic due to the large solvation energies of the charged lysine residues.     

Folding of immunogenic peptide fragments of proteins in water solution. II. The nascent helix

1H nuclear magnetic resonance experiments indicate formation of secondary structures in water solutions of a synthetic immunogenic peptide of sequence EVVPHKKMHKDFLEKIGGL corresponding to the C-helix (residues 69 to 87) of myohemerythrin. The conformational ensemble consists of a set of turn-like structures, distributed over the C-terminal half of the peptide and rapidly interconverting by way of unfolded states. These structures, termed nascent helix, are stabilized into helical structure with long-range order in water/trifluorethanol mixtures. Circular dichroism measurements confirm the presence of 50% helix in water/trifluoroethanol but show no evidence of helicity in water solutions of the peptide. It is apparent that no one member of the transient set of helical conformations which constitutes the nascent helix is sufficiently long to be detectable by circular dichroism experiments. No preferred conformations could be detected by nuclear magnetic resonance in the N-terminal half of the peptide, either in water or water/trifluoroethanol mixtures. This region of the peptide is stabilized in helix by long-range interactions in the folded protein. The possible role of nascent secondary structure in induction of antipeptide antibodies and in initiation of protein folding is discussed.     

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

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

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.     

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.     

Modular design of synthetic protein mimics. Characterization of the helical conformation of a 13-residue peptide in crystals

The incorporation of alpha-aminoisobutyryl (Aib) residues into peptide sequences facilitates helical folding. Aib-containing sequences have been chosen for the design of rigid helical segments in a modular approach to the construction of a synthetic protein mimic. The helical conformation of the synthetic peptide Boc-Aib-(Val-Ala-Leu-Aib)3-OMe in crystals is established by X-ray diffraction. The 13-residue apolar peptide adopts a helical form in the crystal with seven alpha-type hydrogen bonds in the middle and 3(10)-type hydrogen bonds at either end. The helices stack in columns, zigzag rather than linear, by means of direct NH...OC head to tail hydrogen bonds. Leucyl side chains are extended on one side of the helix and valyl side chains on the other side. Water molecules form hydrogen bonds with several backbone carbonyl oxygens that also participate in alpha-helix hydrogen bonds. There is no apparent distortion of the helix caused by hydration. The space group is P2(1)2(1)2(1), with a = 9.964 (3) A, b = 20.117 (3) A, c = 39.311 (6) A, Z = 4, and dx = 1.127 g/cm3 for C64H106N13O16.1.33H2O. The final agreement factor R was 0.089 for 3667 data observed greater than 3 sigma(F) with a resolution of 0.9 A.     

Diffusing and colliding: the atomic level folding/unfolding pathway of a small helical protein

Proteins with ultra-fast folding/unfolding kinetics are excellent candidates for study by molecular dynamics. Here, we describe such simulations of a three helix bundle protein, the engrailed homeodomain (En-HD), which folds via the diffusion-collision model. The unfolding pathway of En-HD was characterized by seven simulations of the protein and 12 simulations of its helical fragments yielding over 1.1 micros of simulation time in water. Various conformational states along the unfolding pathway were identified. There is the compact native-like transition state, a U-shaped helical intermediate and an unfolded state with dynamic helical segments. Each of these states is in good agreement with experimental data. Examining these states as well as the transitions between them, we find the role of long-range tertiary contacts, specifically salt-bridges, important in the folding/unfolding pathway. In the folding direction, charged residues form long-range tertiary contacts before the hydrophobic core is formed. The formation of HII is assisted by a specific salt-bridge and by non-specific (fluctuating) tertiary contacts, which we call contact-assisted helix formation. Salt-bridges persist as the protein approaches the transition state, stabilizing HII until the hydrophobic core is formed. To complement this information, simulations of fragments of En-HD illustrate the helical propensities of the individual segments. By thermal denaturation, HII proved to be the least stable helix, unfolding in less than 450 ps at high temperature. We observed the low helical propensity of C-terminal residues from HIII in fragment simulations which, when compared to En-HD unfolding simulations, link the unraveling of HIII to the initial event that drives the unfolding of En-HD.     

Molecular dynamics simulations of synthetic peptide folding

Because the time scale of protein folding is much greater than that of the widely used simulations of native structures, a detailed report of molecular dynamics simulations of folding has not been available. In this study, we Included the average solvent effect in the potential functions to simplify the calculation of the solvent effect and carried out long molecular dynamics simulations of the alanine-based synthetic peptides at 274 K. From either an extended or a randomly generated conformation, the simulations approached a helix-coil equilibrium in about 3 ns. The multiple minima problem did not prevent helix folding. The calculated helical ratio of Ac-AAQAAAAQAAAAQAAY-NH₂ was 47%, in good agreement with the circular dichroism measurement (about 50%). A helical segment with frayed ends was the most stable conformation, but the hydrophobic interaction favored the compact, distorted helix-turn-helix conformations. The transition between the two types of conformations occurred in a much larger time scale than helix propagation. The transient hydrogen bonds between the glutamine side chain and the backbone carbonyl group could reduce the free energy barrier of helix folding and unfolding. The substitution of a single alanine residue in the middle of the peptide with valine or glycine decreased the average helical ratio significantly, in agreement with experimental observations. © 1996 Wiley-Liss, Inc.