Replica-exchange molecular dynamics method for protein folding

Folding of a highly conserved diverging turn motif from the SH3 domain

Recent NMR structural characterization studies showed that a seven-residue segment (FKKGERL) from the src SH3 domain adopts the nativelike diverging type II beta-turn in aqueous solution in support of the prediction based on the I-sites library of sequence structural motifs. We study the conformational variability and folding/unfolding thermodynamics of this peptide in explicit solvent using replica-exchange molecular dynamics simulations, which greatly enhances the sampling of the conformational space. This peptide samples three main free energy basins (nativelike, intermediate, and unfolded) separated by small barriers. The nativelike basin is fractionally populated (DeltaG(300K) = 0.4 kcal/mol) with structures that satisfy a subset of the NMR-derived constraints. The intrinsic stability of the diverging turn is examined in relationship to the nature of three specific contacts: a turn-hydrogen bond, a mainchain-to-sidechain hydrogen bond, and an end-to-end hydrophobic contact. We have carried out simulations of mutants at the highly conserved GE positions in the sequence. The mutation E5D destabilizes the isolated diverging turn motif, contrary to the observation that this mutation stabilizes the fyn SH3 domain. The G4T mutation also destabilizes the isolated diverging turn; however, the extent of destabilization is smaller than that of the reverse mutation in the drk SH3.

A minimal physically realistic protein-like lattice model: designing an energy landscape that ensures all-or-none folding to a unique native state

A simple protein model restricted to the face-centered cubic lattice has been studied. The model interaction scheme includes attractive interactions between hydrophobic (H) residues, repulsive interactions between hydrophobic and polar (P) residues, and orientation-dependent P-P interactions. Additionally, there is a potential that favors extended beta-type conformations. A sequence has been designed that adopts a native structure, consisting of an antiparallel, six-member Greek-key beta-barrel with protein-like structural degeneracy. It has been shown that the proposed model is a minimal one, i.e., all the above listed types of interactions are necessary for cooperative (all-or-none) type folding to the native state. Simulations were performed via the Replica Exchange Monte Carlo method and the numerical data analyzed via a multihistogram method.

Multiplexed-replica exchange molecular dynamics method for protein folding simulation

Simulating protein folding thermodynamics starting purely from a protein sequence is a grand challenge of computational biology. Here, we present an algorithm to calculate a canonical distribution from molecular dynamics simulation of protein folding. This algorithm is based on the replica exchange method where the kinetic trapping problem is overcome by exchanging noninteracting replicas simulated at different temperatures. Our algorithm uses multiplexed-replicas with a number of independent molecular dynamics runs at each temperature. Exchanges of configurations between these multiplexed-replicas are also tried, rendering the algorithm applicable to large-scale distributed computing (i.e., highly heterogeneous parallel computers with processors having different computational power). We demonstrate the enhanced sampling of this algorithm by simulating the folding thermodynamics of a 23 amino acid miniprotein. We show that better convergence is achieved compared to constant temperature molecular dynamics simulation, with an efficient scaling to large number of computer processors. Indeed, this enhanced sampling results in (to our knowledge) the first example of a replica exchange algorithm that samples a folded structure starting from a completely unfolded state.

beta-Hairpins, alpha-helices, and the intermediates among the secondary structures in the energy landscape of a peptide from a distal beta-hairpin of SH3 domain

Energy landscape of a peptide, extracted from a distal beta-hairpin of src SH3 domain, in explicit water was obtained with the multicanonical molecular dynamics. A variety of beta-hairpins with various strand-strand hydrogen bonds were found in the energy landscape at 300 K. There was no energy barrier between random-coil and hairpins. Thus, the peptide conformation can easily change from the random-coil to the hairpins in the thermal fluctuations at 300 K. The landscape also included two clusters of alpha-helices, among which an energy barrier existed, and besides, these helix clusters were separated from the other conformations. Thus, the free-energy barrier exists among the helices and the other conformations. Intermediate clusters were found between the helix and the hairpin clusters. The current study showed that the isolated state of this peptide in water fluctuates among random-coil, beta-hairpin, and alpha-helix. In SH3 domain, which has a topology of mainly beta-protein, the whole-protein folding may proceed when the segment is folded in the beta-hairpin and the other parts of the protein are coupled with the beta-hairpin in an energetically or kinetically favorite way.

Hybrid Monte Carlo with multidimensional replica exchanges: conformational equilibria of the hypervariable regions of a llama VHH antibody domain

Since the structural repertoire of the hypervariable regions of human antibodies is known to be more restricted than what is implied by sequence variability, a common approach to structural prediction is to use a knowledge-based (KB) method, such as the canonical structure model (C. Chothia and A. M. Lesk, Journal of Molecular Biology, 1987, Vol. 196, pp. 901-917). However, this model is less successful when applied to camelid heavy chain antibodies. In this study, molecular simulations were used to examine the conformational equilibria of the hypervariable regions (H1, H2, and H3) of a llama heavy chain variable domain, for which KB predictions are poor. Simulations were carried out using both conventional molecular dynamics (MD) and hybrid Monte Carlo with multidimensional replica exchanges (HYMREX). The advantage of the latter method is its ability to selectively target parts of the Hamiltonian that can most readily improve sampling. A novel variant of HYMREX was implemented in which, besides the temperature, torsional interactions and the range of nonbonded interactions were varied. To compare the sampling abilities of MD and this HYMREX scheme, simulations were started from a misfolded conformational state. Overall, MD yielded final conformations more similar to the initial state, implying quasi-ergodic sampling. In contrast, HYMREX achieved more ergodic sampling, and the majority of conformations that it sampled agreed well with the known crystal structure. The HYMREX simulation results were used to help identify the chief interactions governing the conformational equilibria and to reexamine the key assumptions underlying the KB predictions. The data show that the H1 region exhibited significant conformational freedom, in support of the hypothesis that main-chain structural variability in this region could play a greater role in antigen binding in camelid antibodies than it does in normal antibodies. Key H1 residues and associated inter-loop interactions are conjectured to account for the poor KB predictions.

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.

Dynamical origin of uniform sampling in multicanonical ensemble

The stochastic model describing the sampling process in multicanonical ensemble has been derived by considering the sampling process as an overdamped Brownian motion on the free energy surface. The essential dynamics of the multicanonical sampling has been characterized by a Langevin equation in a piecewise multivalleyed free energy landscape, modulated by a temperature-dependent curvature. Based on the stochastic model we showed that the multicanonical weight can be determined by interpolating maximum probability energy points of the canonical samplings at different temperatures.

The origins of asymmetry in the folding transition states of protein L and protein G

Topology has been shown to be an important determinant of many features of protein folding; however, the delineation of sequence effects on folding remains obscure. Furthermore, differentiation between the two influences proves difficult due to their intimate relationship. To investigate the effect of sequence in the absence of significant topological differences, we examined the folding mechanisms of segment B1 peptostreptococcal protein L and segment B1 of streptococcal protein G. These proteins share the same highly symmetrical topology. Despite this symmetry, neither protein folds through a symmetrical transition state. We analyzed the origins of this difference using theoretical models. We found that the strength of the interactions present in the N-terminal hairpin of protein L causes this hairpin to form ahead of the C-terminal hairpin. The difference in chain entropy associated with the formation of the hairpins of protein G proves sufficient to beget initiation of folding at the shorter C-terminal hairpin. Our findings suggest that the mechanism of folding may be understood by examination of the free energy associated with the formation of partially folded microstates.

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.

Can a continuum solvent model reproduce the free energy landscape of a beta -hairpin folding in water?

The folding free energy landscape of the C-terminal beta-hairpin of protein G is explored using the surface-generalized Born (SGB) implicit solvent model, and the results are compared with the landscape from an earlier study with explicit solvent model. The OPLSAA force field is used for the beta-hairpin in both implicit and explicit solvent simulations, and the conformational space sampling is carried out with a highly parallel replica-exchange method. Surprisingly, we find from exhaustive conformation space sampling that the free energy landscape from the implicit solvent model is quite different from that of the explicit solvent model. In the implicit solvent model some nonnative states are heavily overweighted, and more importantly, the lowest free energy state is no longer the native beta-strand structure. An overly strong salt-bridge effect between charged residues (E42, D46, D47, E56, and K50) is found to be responsible for this behavior in the implicit solvent model. Despite this, we find that the OPLSAA/SGB energies of all the nonnative structures are higher than that of the native structure; thus the OPLSAA/SGB energy is still a good scoring function for structure prediction for this beta-hairpin. Furthermore, the beta-hairpin population at 282 K is found to be less than 40% from the implicit solvent model, which is much smaller than the 72% from the explicit solvent model and approximately equal 80% from experiment. On the other hand, both implicit and explicit solvent simulations with the OPLSAA force field exhibit no meaningful helical content during the folding process, which is in contrast to some very recent studies using other force fields.

Monte Carlo simulations of the peptide recognition at the consensus binding site of the constant fragment of human immunoglobulin G: the energy landscape analysis of a hot spot at the intermolecular interface

Monte Carlo simulations of molecular recognition at the consensus binding site of the constant fragment (Fc) of human immunoglobulin G (Ig) protein have been performed to analyze structural and thermodynamic aspects of binding for the 13-residue cyclic peptide DCAWHLGELVWCT. The energy landscape analysis of a hot spot at the intermolecular interface using alanine scanning and equilibrium-simulated tempering dynamics with the simplified, knowledge-based energy function has enabled the role of the protein hot spot residues in providing the thermodynamic stability of the native structure to be determined. We have found that hydrophobic interactions between the peptide and the Met-252, Ile-253, His-433, and His-435 protein residues are critical to guarantee the thermodynamic stability of the crystallographic binding mode of the complex. Binding free energy calculations, using a molecular mechanics force field and a solvation energy model, combined with alanine scanning have been conducted to determine the energetic contribution of the protein hot spot residues in binding affinity. The conserved Asn-434, Ser-254, and Tyr-436 protein residues contribute significantly to the binding affinity of the peptide-protein complex, serving as an energetic hot spot at the intermolecular interface. The results suggest that evolutionary conserved hot spot protein residues at the intermolecular interface may be partitioned in fulfilling thermodynamic stability of the native binding mode and contributing to the binding affinity of the complex.

Molecular dynamics study of peptides in implicit water: ab initio folding of beta-hairpin, beta-sheet, and beta beta alpha-motif

In this communication, we have demonstrated that molecular dynamics simulations using a GB implicit solvation model with the all-atom based force field (CHARMM19) can describe the spontaneous folding of small peptides in aqueous solution. The native structures of peptides with various structural motifs (beta-hairpin, beta-sheet, and betabetaalpha-moiety) were successfully predicted within reasonable time scales by MD simulations at moderately elevated temperatures. It is expected that the present simulations provide further insight into mechanism/pathways of the peptide folding.

Alpha-helical stabilization by side chain shielding of backbone hydrogen bonds

We study atomic models of the thermodynamics of the structural transition of peptides that form alpha-helices. The effect of sequence variation on alpha-helix formation for alanine-rich peptides, Ac-Ala21-methyl amide (A21) and Ac-A5 (AAARA)3A-methyl amide (Fs peptide), is investigated by atomic simulation studies of the thermodynamics of the helix-coil transition in explicit water. The simulations show that the guanidinium group in the Arg side chains in the Fs peptide interacts with the carbonyl group four amino acids upstream in the chain and desolvates backbone hydrogen bonds. This desolvation can be directly correlated with a higher probability of hydrogen bond formation. We find that Fs has higher helical content than A21 at all temperatures. A small modification in the amber force field reproduces the experimental helical content and helix-coil transition temperatures for the Fs peptide.

Structure of Met-enkephalin in explicit aqueous solution using replica exchange molecular dynamics

Replica exchange molecular dynamics (MD) simulations of Met-enkephalin in explicit solvent reveal helical and nonhelical structures. Four predominant structures of Met-enkephalin are sampled with comparable probabilities (two helical and two nonhelical). The energy barriers between these configurations are low, suggesting that Met-enkephalin switches easily between configurations. This is consistent with the requirement that Met-enkephalin be sufficiently flexible to bind to several different receptors. Replica exchange simulations of 32 ns are shown to sample approximately five times more configurational space than constant temperature MD simulations of the same duration. The energy landscape for the replica exchange simulation is presented. A detailed study of replica trajectories demonstrates that the significant increases in temperature provided by the replica exchange technique enable transitions from nonhelical to helical structures that would otherwise be prevented by kinetic trapping. Met-enkephalin (Type Entrez Proteins; Value A61445; Service Entrez Proteins).

Hierarchy of simulation models in predicting structure and energetics of the Src SH2 domain binding to tyrosyl phosphopeptides

Structure and energetics of the Src Src Homology 2 (SH2) domain binding with the recognition phosphopeptide pYEEI and its mutants are studied by a hierarchical computational approach. The proposed structure prediction strategy includes equilibrium sampling of the peptide conformational space by simulated tempering dynamics with the simplified, knowledge-based energy function, followed by structural clustering of the resulting conformations and binding free energy evaluation of a single representative from each cluster, a cluster center. This protocol is robust in rapid screening of low-energy conformations and recovers the crystal structure of the pYEEI peptide. Thermodynamics of the peptide-SH2 domain binding is analyzed by computing the average energy contributions over conformations from the clusters, structurally similar to the predicted peptide bound structure. Using this approach, the binding thermodynamics for a panel of studied peptides is predicted in a better agreement with the experiment than previously suggested models. However, the overall correlation between computed and experimental binding affinity remains rather modest. The results of this study show that small differences in binding free energies between the Ala and Gly mutants of the pYEEI peptide are considerably more difficult to predict than the structure of the bound peptides, indicating that accurate computational prediction of binding affinities still remains a major methodological and technical challenge.

The free energy landscape for beta hairpin folding in explicit water

The folding free energy landscape of the C-terminal beta hairpin of protein G has been explored in this study with explicit solvent under periodic boundary condition and OPLSAA force field. A highly parallel replica exchange method that combines molecular dynamics trajectories with a temperature exchange Monte Carlo process is used for sampling with the help of a new efficient algorithm P3ME/RESPA. The simulation results show that the hydrophobic core and the beta strand hydrogen bond form at roughly the same time. The free energy landscape with respect to various reaction coordinates is found to be rugged at low temperatures and becomes a smooth funnel-like landscape at about 360 K. In contrast to some very recent studies, no significant helical content has been found in our simulation at all temperatures studied. The beta hairpin population and hydrogen-bond probability are in reasonable agreement with the experiment at biological temperature, but both decay more slowly than the experiment with temperature.

Energy landscape of a peptide consisting of alpha-helix, 3(10)-helix, beta-turn, beta-hairpin, and other disordered conformations

The energy landscape of a peptide [Ace-Lys-Gln-Cys-Arg-Glu-Arg-Ala-Nme] in explicit water was studied with a multicanonical molecular dynamics simulation, and the AMBER parm96 force field was used for the energy calculation. The peptide was taken from the recognition helix of the DNA-binding protein, c-MYB: A rugged energy landscape was obtained, in which the random-coil conformations were dominant at room temperature. The CD spectra of the synthesized peptide revealed that it is in the random state at room temperature. However, the 300 K canonical ensemble, Q(300K), contained alpha-helix, 3(10)-helix, beta-turn, and beta-hairpin structures with small but notable probabilities of existence. The complete alpha-helix, imperfect alpha-helix, and random-coil conformations were separated from one another in the conformational space. This means that the peptide must overcome energy barriers to form the alpha-helix. The overcoming process may correspond to the hydrogen-bond rearrangements from peptide-water to peptide-peptide interactions. The beta-turn, imperfect 3(10)-helix, and beta-hairpin structures, among which there are no energy barriers at 300 K, were embedded in the ensemble of the random-coil conformations. Two types of beta-hairpin with different beta-turn regions were observed in Q(300K). The two beta-hairpin structures may have different mechanisms for the beta-hairpin formation. The current study proposes a scheme that the random state of this peptide consists of both ordered and disordered conformations. In contrast, the energy landscape obtained from the parm94 force field was funnel like, in which the peptide formed the helical conformation at room temperature and random coil at high temperature.

Generalized-ensemble algorithms for molecular simulations of biopolymers

In complex systems with many degrees of freedom such as peptides and proteins, there exists a huge number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present three new generalized-ensemble algorithms that combine the merits of the above methods. The effectiveness of the methods for molecular simulations in the protein folding problem is tested with short peptide systems.

Exploring the energy landscape of a beta hairpin in explicit solvent

We studied the energy landscape of the peptide Ace-GEWTYDDATKTFTVTE-Nme, taken from the C-terminal fragment (41-56) of protein G, in explicit aqueous solution by a highly parallel replica-exchange approach that combines molecular dynamics trajectories with a temperature exchange Monte Carlo process. The combined trajectories in T and configurational space allow a replica to overcome a free energy barrier present at one temperature by increasing T, changing configurations, and cooling in a self-regulated manner, thus allowing sampling of broad regions of configurational space in short (nanoseconds) time scales. The free energy landscape of this system over a wide range of temperatures shows that the system preferentially adopts a beta hairpin structure. However, the peptide also samples other stable ensembles where the peptide adopts helices and helix-turn-helix states, among others. The helical states become increasingly stable at low temperatures, but are slightly less stable than the beta turn ensemble. The energy landscape is rugged at low T, where substates are separated by large energy barriers. These barriers disappear at higher T (approximately 330 K), where the system preferentially adopts a "molten globule" state with structures similar to the beta hairpin.

Replica-exchange molecular dynamics simulation for supercooled liquids

We investigate to what extend the replica-exchange Monte Carlo method is able to equilibrate a simple liquid in its supercooled state. We find that this method does indeed allow us to generate accurately the canonical distribution function even at low temperatures and that its efficiency is about 10-100 times higher than the usual canonical molecular dynamics simulation.