Molecular dynamics simulations of beta-hairpin folding

Molecular dynamics simulations of beta-hairpin folding have been carried out with a solvent-referenced potential at 274 K. The model peptide V4DPGV4 formed stable beta-hairpin conformations and the beta-hairpin ratio calculated by the DSSP algorithm was about 56% in the 50-ns simulation. Folding into beta-hairpin conformations is independent of the initial conformations. The simulations provided insights into the folding mechanism. The hydrogen bond often formed in a beta-turn first, and then propagated by forming more hydrogen bonds along the strands. Unfolding and refolding occurred repeatedly during the simulations. Both the hydrogen bonding and the hydrophobic interaction played important roles in forming the ordered structure. Without the hydrophobic effect, stable beta-hairpin conformations did not form in the simulations. With the same energy functions, the alanine-based peptide (AAQAA)3Y folded into helical conformations, in agreement with experiments. Folding into an alpha-helix or a beta-hairpin is amino acid sequence-dependent.     

Cooperative folding mechanism of a beta-hairpin peptide studied by a multicanonical replica-exchange molecular dynamics simulation

G-peptide is a 16-residue peptide of the C-terminal end of streptococcal protein G B1 domain, which is known to fold into a specific beta-hairpin within 6 micros. Here, we study molecular mechanism on the stability and folding of G-peptide by performing a multicanonical replica-exchange (MUCAREM) molecular dynamics simulation with explicit solvent. Unlike the preceding simulations of the same peptide, the simulation was started from an unfolded conformation without any experimental information on the native conformation. In the 278-ns trajectory, we observed three independent folding events. Thus MUCAREM can be estimated to accelerate the folding reaction more than 60 times than the conventional molecular dynamics simulations. The free-energy landscape of the peptide at room temperature shows that there are three essential subevents in the folding pathway to construct the native-like beta-hairpin conformation: (i) a hydrophobic collapse of the peptide occurs with the side-chain contacts between Tyr45 and Phe52, (ii) then, the native-like turn is formed accompanying with the hydrogen-bonded network around the turn region, and (iii) finally, the rest of the backbone hydrogen bonds are formed. A number of stable native hydrogen bonds are formed cooperatively during the second stage, suggesting the importance of the formation of the specific turn structure. This is also supported by the accumulation of the nonnative conformations only with the hydrophobic cluster around Tyr45 and Phe52. These simulation results are consistent with high phi-values of the turn region observed by experiment.     

Molecular dynamics simulations of a beta-hairpin fragment of protein G: balance between side-chain and backbone forces

How is the native structure encoded in the amino acid sequence? For the traditional backbone centric view, the dominant forces are hydrogen bonds (backbone) and phi-psi propensity. The role of hydrophobicity is non-specific. For the side-chain centric view, the dominant force of protein folding is hydrophobicity. In order to understand the balance between backbone and side-chain forces, we have studied the contributions of three components of a beta-hairpin peptide: turn, backbone hydrogen bonding and side-chain interactions, of a 16-residue fragment of protein G. The peptide folds rapidly and cooperatively to a conformation with a defined secondary structure and a packed hydrophobic cluster of aromatic side-chains. Our strategy is to observe the structural stability of the beta-hairpin under systematic perturbations of the turn region, backbone hydrogen bonds and the hydrophobic core formed by the side-chains, respectively. In our molecular dynamics simulations, the peptides are solvated. with explicit water molecules, and an all-atom force field (CFF91) is used. Starting from the original peptide (G41EWTYDDATKTFTVTE56), we carried out the following MD simulations. (1) unfolding at 350 K; (2) forcing the distance between the C(alpha) atoms of ASP47 and LYS50 to be 8 A; (3) deleting two turn residues (Ala48 and Thr49) to form a beta-sheet complex of two short peptides, GEWTYDD and KTFTVTE; (4) four hydrophobic residues (W43, Y45, F52 and T53) are replaced by a glycine residue step-by-step; and (5) most importantly, four amide hydrogen atoms (T44, D46, T53, and T55, which are crucial for backbone hydrogen bonding), are substituted by fluorine atoms. The fluorination not only makes it impossible to form attractive hydrogen bonding between the two beta-hairpin strands, but also introduces a repulsive force between the two strands due to the negative charges on the fluorine and oxygen atoms. Throughout all simulations, we observe that backbone hydrogen bonds are very sensitive to the perturbations and are easily broken. In contrast, the hydrophobic core survives most perturbations. In the decisive test of fluorination, the fluorinated peptide remains folded under our simulation conditions (5 ns, 278 K). Hydrophobic interactions keep the peptide folded, even with a repulsive force between the beta-strands. Thus, our results strongly support a side-chain centric view for protein folding.     

Effects of Turn Stability and Side-Chain Hydrophobicity on the Folding of β-Structures

Key elements of β-structure folding include hydrophobic core collapse, turn formation, and assembly of backbone hydrogen bonds. In the present folding simulations of several β-hairpins and β-sheets (peptide 1, protein G B1 domain peptide, TRPZIP2, TRPZIP4, 20mer, and 20mer^DP6D), the folding free-energy landscape as a function of several reaction coordinates corresponding to the three key elements indicates apparent dependence on turn stability and side-chain hydrophobicity, which demonstrates different folding mechanisms of similar β-structures of varied sequences. Turn stability is found to be the key factor in determining the formation order of the three structural elements in the folding of β-structures. Moreover, turn stability and side-chain hydrophobicity both affect the stability of backbone hydrogen bonds. The three-stranded β-sheets fold through a three-state transition in which the formation of one hairpin always takes precedence over the other. The different stabilities of two anti-parallel hairpins in each three-stranded β-sheet are shown to correlate well with the different levels of their hydrophobic interactions.     

Complex folding pathways in a simple beta-hairpin

The determination of the folding mechanisms of proteins is critical to understand the topological change that can propagate Alzheimer and Creutzfeld-Jakobs diseases, among others. The computational community has paid considerable attention to this problem; however, the associated time scale, typically on the order of milliseconds or more, represents a formidable challenge. Ab initio protein folding from long molecular dynamics simulations or ensemble dynamics is not feasible with ordinary computing facilities and new techniques must be introduced. Here we present a detailed study of the folding of a 16-residue beta-hairpin, described by a generic energy model and using the activation-relaxation technique. From a total of 90 trajectories at 300 K, three folding pathways emerge. All involve a simultaneous optimization of the complete hydrophobic and hydrogen bonding interactions. The first two pathways follow closely those observed by previous theoretical studies (folding starting at the turn or by interactions between the termini). The third pathway, never observed by previous all-atom folding, unfolding, and equilibrium simulations, can be described as a reptation move of one strand of the beta-sheet with respect to the other. This reptation move indicates that non-native interactions can play a dominant role in the folding of secondary structures. Furthermore, such a mechanism mediated by non-native hydrogen bonds is not available for study by unfolding and Gō model simulations. The exact folding path followed by a given beta-hairpin is likely to be influenced by its sequence and the solvent conditions. Taken together, these results point to a more complex folding picture than expected for a simple beta-hairpin.     

Understanding the mechanism of beta-hairpin folding via phi-value analysis

The folding kinetics of a 16-residue beta-hairpin (trpzip4) and five mutants were studied by a laser-induced temperature-jump infrared method. Our results indicate that mutations which affect the strength of the hydrophobic cluster lead to a decrease in the thermal stability of the beta-hairpin, as a result of increased unfolding rates. For example, the W45Y mutant has a phi-value of approximately zero, implying a folding transition state in which the native contacts involving Trp45 are not yet formed. On the other hand, mutations in the turn or loop region mostly affect the folding rate. In particular, replacing Asp46 with Ala leads to a decrease in the folding rate by roughly 9 times. Accordingly, the phi-value for D46A is determined to be approximately 0.77, suggesting that this residue plays a key role in stabilizing the folding transition state. This is most likely due to the fact that the main chain and side chain of Asp46 form a characteristic hydrogen bond network with other residues in the turn region. Taken together, these results support the folding mechanism we proposed before, which suggests that the turn formation is the rate-limiting step in beta-hairpin folding and, consequently, a stronger turn-promoting sequence increases the stability of a beta-hairpin primarily by increasing its folding rate, whereas a stronger hydrophobic cluster increases the stability of a beta-hairpin primarily by decreasing its unfolding rate. In addition, we have examined the compactness of the thermally denatured and urea-denatured states of another 16-residue beta-hairpin, using the method of fluorescence resonance energy transfer. Our results show that the thermally denatured state of this beta-hairpin is significantly more compact than the urea-denatured state, suggesting that the very first step in beta-hairpin folding, when initiated from an extended conformation, probably corresponds to a process of hydrophobic collapse.     

Understanding beta-hairpin formation by molecular dynamics simulations of unfolding

We have studied the mechanism of formation of a 16-residue beta-hairpin from the protein GB1 using molecular dynamics simulations in an aqueous environment. The analysis of unfolding trajectories at high temperatures suggests a refolding pathway consisting of several transient intermediates. The changes in the interaction energies of residues are related with the structural changes during the unfolding of the hairpin. The electrostatic energies of the residues in the turn region are found to be responsible for the transition between the folded state and the hydrophobic core state. The van der Waals interaction energies of the residues in the hydrophobic core reflect the behavior of the radius of gyration of the core region. We have examined the opposing influences of the protein-protein (PP) energy, which favors the native state, and the protein-solvent (PS) energy, which favors unfolding, in the formation of the beta-hairpin structure. It is found that the behavior of the electrostatic components of PP and PS energies reflects the structural changes associated with the loss of backbone hydrogen bonding. Relative changes in the PP and PS van der Waals interactions are related with the disruption of the hydrophobic core of a protein. The results of the simulations support the hydrophobic collapse mechanism of beta-hairpin folding.     

Folding thermodynamics of three beta-sheet peptides: a model study

We study the folding thermodynamics of a beta-hairpin and two three-stranded beta-sheet peptides using a simplified sequence-based all-atom model, in which folding is driven mainly by backbone hydrogen bonding and effective hydrophobic attraction. The native populations obtained for these three sequences are in good agreement with experimental data. We also show that the apparent native population depends on which observable is studied; the hydrophobicity energy and the number of native hydrogen bonds give different results. The magnitude of this dependence matches well with the results obtained in two different experiments on the beta-hairpin.     

beta-hairpin stability and folding: molecular dynamics studies of the first beta-hairpin of tendamistat

The stability and (un)folding of the 19-residue peptide, SCVTLYQSWRYSQADNGCA, corresponding to the first beta-hairpin (residues 10 to 28) of the alpha-amylase inhibitor tendamistat (PDB entry 3AIT) has been studied by molecular dynamics simulations in explicit water under periodic boundary conditions at several temperatures (300 K, 360 K and 400 K), starting from various conformations for simulation lengths, ranging from 10 to 30 ns. Comparison of trajectories of the reduced and oxidized native peptides reveals the importance of the disulphide bridge closing the beta-hairpin in maintaining a proper turn conformation, thereby insuring a proper side-chain arrangement of the conserved turn residues. This allows rationalization of the conservation of those cysteine residues among the family of alpha-amylase inhibitors. High temperature simulations starting from widely different initial configurations (native beta-hairpin, alpha and left-handed helical and extended conformations) begin sampling similar regions of the conformational space within tens of nanoseconds, and both native and non-native beta-hairpin conformations are recovered. Transitions between conformational clusters are accompanied by an increase in energy fluctuations, which is consistent with the increase in heat capacity measured experimentally upon protein folding. The folding events observed in the various simulations support a model for beta-hairpin formation in which the turn is formed first, followed by hydrogen bond formation closing the hairpin, and subsequent stabilization by side-chain hydrophobic interactions.     

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.     

Free energy landscape and folding mechanism of a beta-hairpin in explicit water: a replica exchange molecular dynamics study

The free energy landscape and the folding mechanism of the C-terminal beta-hairpin of protein G is studied by extensive replica exchange molecular dynamics simulations (40 replicas and 340 ns total simulation time), using the GROMOS96 force field and the SPC explicit water solvent. The study reveals that the system preferentially adopts a beta-hairpin structure at biologically important temperatures, and that the helix content is low at all temperatures studied. Representing the free energy landscape as a function of several types of reaction coordinates, four local minima corresponding to the folded, partially folded, molten globule, and unfolded states are identified. The findings suggest that the folding of the beta-hairpin occurs as the sequence: collapse of hydrophobic core --> formation of H-bond --> formation of the turn. Identifying the folded and molten globule states as the main conformations, the free energy landscape of the beta-hairpin is consistent with a two-state behavior with a broad transition state. The temperature dependence of the folding-unfolding transition is investigated in some detail. The enthalpy and entropy jumps at the folding transition temperature are found to be about three times lower than the experimental estimates, indicating that the folding-unfolding transition in silico is less cooperative than its in vitro counterpart.     

Solvent effects on the conformational transition of a model polyalanine peptide

We have investigated the folding of polyalanine by combining discontinuous molecular dynamics simulation with our newly developed off-lattice intermediate-resolution protein model. The thermodynamics of a system containing a single Ac-KA(14)K-NH(2) molecule has been explored by using the replica exchange simulation method to map out the conformational transitions as a function of temperature. We have also explored the influence of solvent type on the folding process by varying the relative strength of the side-chain's hydrophobic interactions and backbone hydrogen bonding interactions. The peptide in our simulations tends to mimic real polyalanine in that it can exist in three distinct structural states: alpha-helix, beta-structures (including beta-hairpin and beta-sheet-like structures), and random coil, depending upon the solvent conditions. At low values of the hydrophobic interaction strength between nonpolar side-chains, the polyalanine peptide undergoes a relatively sharp transition between an alpha-helical conformation at low temperatures and a random-coil conformation at high temperatures. As the hydrophobic interaction strength increases, this transition shifts to higher temperatures. Increasing the hydrophobic interaction strength even further induces a second transition to a beta-hairpin, resulting in an alpha-helical conformation at low temperatures, a beta-hairpin at intermediate temperatures, and a random coil at high temperatures. At very high values of the hydrophobic interaction strength, polyalanines become beta-hairpins and beta-sheet-like structures at low temperatures and random coils at high temperatures. This study of the folding of a single polyalanine-based peptide sets the stage for a study of polyalanine aggregation in a forthcoming paper.     

Molecular dynamics simulations of folding processes of a beta-hairpin in an implicit solvent

Computer simulations of beta-hairpin folding are relatively difficult, especially those based on the explicit water model. This greatly limits the complete analysis and understanding of their folding mechanisms. In this paper, we use the generalized Born/solvent accessible implicit solvent model to simulate the folding processes of a nine-residue beta-hairpin. We find that the beta-hairpin can fold into its native structure very easily, even using the traditional molecular dynamics method. This allows us to extract 21 complete folding events and investigate the folding process sufficiently. Our results show that there exist four most stable states on the free energy landscape of the short peptide, one native state and three intermediates. We find that two of the non-native stable states have almost the same potential energy as the native state but with lower entropy. This suggests that the native state can be stabilized entropically. Furthermore, we find that the folding processes of this peptide have common features: to fold into its native state, the peptide undergoes a continuous collapsing-extending-recollapsing process to adjust the positions of the side chains in order to form the native middle inter-strand hydrogen bonds. The formations of these bonds are the key step of the folding process. Once these bonds are formed, the peptide can fold into the native state quickly.     

Beta-hairpin folding simulations in atomistic detail using an implicit solvent model

We have used distributed computing techniques and a supercluster of thousands of computer processors to study folding of the C-terminal beta-hairpin from protein G in atomistic detail using the GB/SA implicit solvent model at 300 K. We have simulated a total of nearly 38 micros of folding time and obtained eight complete and independent folding trajectories. Starting from an extended state, we observe relaxation to an unfolded state characterized by non-specific, temporary hydrogen bonding. This is followed by the appearance of interactions between hydrophobic residues that stabilize a bent intermediate. Final formation of the complete hydrophobic core occurs cooperatively at the same time that the final hydrogen bonding pattern appears. The folded hairpin structures we observe all contain a closely packed hydrophobic core and proper beta-sheet backbone dihedral angles, but they differ in backbone hydrogen bonding pattern. We show that this is consistent with the existing experimental data on the hairpin alone in solution. Our analysis also reveals short-lived semi-helical intermediates which define a thermodynamic trap. Our results are consistent with a three-state mechanism with a single rate-limiting step in which a varying final hydrogen bond pattern is apparent, and semi-helical off-pathway intermediates may appear early in the folding process. We include details of the ensemble dynamics methodology and a discussion of our achievements using this new computational device for studying dynamics at the atomic level.     

Conformational transition states of a beta-hairpin peptide between the ordered and disordered conformations in explicit water

The conformational transition states of a beta-hairpin peptide in explicit water were identified from the free energy landscapes obtained from the multicanonical ensemble, using an enhanced conformational sampling calculation. The beta-hairpin conformations were significant at 300 K in the landscape, and the typical nuclear Overhauser effect signals were reproduced, consistent with the previously reported experiment. In contrast, the disordered conformations were predominant at higher temperatures. Among the stable conformations at 300 K, there were several free energy barriers, which were not visible in the landscapes formed with the conventional parameters. We identified the transition states around the saddle points along the putative folding and unfolding paths between the beta-hairpin and the disordered conformations in the landscape. The characteristic features of these transition states are the predominant hydrophobic contacts and the several hydrogen bonds among the side-chains, as well as some of the backbone hydrogen bonds. The unfolding simulations at high temperatures, 400 K and 500 K, and their principal component analyses also provided estimates for the transition state conformations, which agreed well with those at 400 K and 500 K deduced from the current free energy landscapes at 400 K and 500 K, respectively. However, the transition states at high temperatures were much more widely distributed on the landscape than those at 300 K, and their conformations were different.     

The mechanism of beta-hairpin formation

Beta-hairpins constitute an important class of connecting protein secondary structures. Several groups have postulated that such structures form early in the folding process and serve to nucleate the formation of extended beta-sheet structures. Despite the importance of beta-hairpins in protein folding, little is known about the mechanism of formation of these structures. While it is well established that there is a complex interplay between the stability of a beta-hairpin and loop conformational propensity, loop length, and the formation of stabilizing cross-strand interactions (H-bonds and hydrophobic interactions), the influence of these factors on the folding rate is poorly understood. Peptide models provide a simple framework for exploring the molecular details of the formation of beta-hairpin structures. We have explored the fundamental processes of folding in two linear peptides that form beta-hairpin structures, having a stabilizing hydrophobic cluster connected by loops of differing lengths. This approach allows us to evaluate existing models of the mechanism of beta-hairpin formation. We find a substantial acceleration of the folding rate when the connecting loop is made shorter (i.e., the hydrophobic cluster is moved closer to the turn). Analysis of the folding kinetics of these two peptides reveals that this acceleration is a direct consequence of the reduced entropic cost of the smaller loop search.     

A breakdown of symmetry in the folding transition state of protein L

The 62 residue IgG binding domain of protein L consists of a central alpha-helix packed on a four-stranded beta-sheet formed by N and C-terminal beta-hairpins. The overall topology of the protein is quite symmetric: the beta-hairpins have similar lengths and make very similar interactions with the central helix. Characterization of the effects of 70 point mutations distributed throughout the protein on the kinetics of folding and unfolding reveals that this symmetry is completely broken during folding; the first beta-hairpin is largely structured while the second beta-hairpin and helix are largely disrupted in the folding transition state ensemble. The results are not consistent with a "hydrophobic core first" picture of protein folding; the first beta-hairpin appears to be at least as ordered at the rate limiting step in folding as the hydrophobic core.     

A molecular dynamics study of the 41-56 beta-hairpin from B1 domain of protein G.

The structural and dynamical behavior of the 41-56 beta-hairpin from the protein G B1 domain (GB1) has been studied at different temperatures using molecular dynamics (MD) simulations in an aqueous environment. The purpose of these simulations is to establish the stability of this hairpin in view of its possible role as a nucleation site for protein folding. The conformation of the peptide in the crystallographic structure of the protein GB1 (native conformation) was lost in all simulations. The new equilibrium conformations are stable for several nanoseconds at 300K (>10 ns), 350 K (>6.5 ns), and even at 450 K (up to 2.5 ns). The new structures have very similar hairpin-like conformations with properties in agreement with available experimental nuclear Overhauser effect (NOE) data. The stability of the structure in the hydrophobic core region during the simulations is consistent with the experimental data and provides further evidence for the role played by hydrophobic interactions in hairpin structures. Essential dynamics analysis shows that the dynamics of the peptide at different temperatures spans basically the same essential subspace. The main equilibrium motions in this subspace involve large fluctuations of the residues in the turn and ends regions. Of the six interchain hydrogen bonds, the inner four remain stable during the simulations. The space spanned by the first two eigenvectors, as sampled at 450 K, includes almost all of the 47 different hairpin structures found in the database. Finally, analysis of the hydration of the 300 K average conformations shows that the hydration sites observed in the native conformation are still well hydrated in the equilibrium MD ensemble.     

Role of hydrophilic and hydrophobic contacts in folding of the second beta-hairpin fragment of protein G: molecular dynamics simulation studies of an all-atom model

Predicting the folding mechanism of the second beta-hairpin fragment of the Ig-binding domain B of streptococcal protein G is unexpectedly challenging for simplified reduced models because the models developed so far indicated a different folding mechanism from what was suggested from high-temperature unfolding and equilibrium free-energy surface analysis based on established all-atom empirical force fields in explicit or implicit solvent. This happened despite the use of empirical residue-based interactions, multibody hydrophobic interactions, and inclusions of hydrogen bonding effects in the simplified models. This article employs a recently developed all-atom (except nonpolar hydrogens) model interacting with simple square-well potentials to fold the peptide fragment by molecular dynamics simulation methods. In this study, 193 out of 200 trajectories are folded at two reduced temperatures (3.5 and 3.7) close to the transition temperature T* approximately 4.0. Each simulation takes <7 h of CPU time on a Pentium 800-MHz PC. Folding of the new all-atom model is found to be initiated by collapse before the formation of main-chain hydrogen bonds. This verifies the mechanism proposed from previous all-atom unfolding and equilibrium simulations. The new model further predicts that the collapse is initiated by two nucleation contacts (a hydrophilic contact between D46 and T49 and a hydrophobic contact between Y45 and F52), in agreement with recent NMR measurements. The results suggest that atomic packing and native contact interactions play a dominant role in folding mechanism.