Folding of alpha(r)beta and epsilonbeta reverse turns; a nanosecond molecular dynamics simulation of the hexapeptide MSALNT and the octapeptide NMSALNTL in water.

Folding of the hexapeptide MSALNT and the octapeptide NMSALNTL were investigated using 2.8 ns molecular dynamics (MD) simulations in aqueous solution. In the simulation, the central sequence SALN of the hexapeptide folded rapidly within 200 ps into an alpha(r)beta turn conformation (type VIII conformation) and remained in this conformation for the rest of the trajectory. The sequence SALN of the octapeptide needed 2 ns to fold via epsilonbeta conformations into a similar conformation. The results join the sequences into a growing group of sequences which have a tendency to form secondary structures and thereby to direct protein folding. The structures of the reverse turn conformations were in accordance with the experimental results (Hakalehto et al., Eur J. Biochem. 250, 19-29 (1997)). The main driving force of folding seems to be the hydrophobic interaction between the side chains of Ala and Leu at the i+1 and i+2 positions of the beta-turn.     

Folding study of an Aib-rich peptide in DMSO by molecular dynamics simulations.

To evaluate the ability of molecular dynamics (MD) simulations using atomic force-fields to correctly predict stable folded conformations of a peptide in solution, we show results from MD simulations of the reversible folding of an octapeptide rich in alpha-aminoisobutyric acid (2-amino-2-methyl-propanoic acid, Aib) solvated in di-methyl-sulfoxide (DMSO). This solvent generally prevents the formation of secondary structure, whereas Aib-rich peptides show a high propensity to form secondary structural elements, in particular 3(10)- and alpha-helical structures. Aib is, moreover, achiral, so that Aib-rich peptides can form left- or right-handed helices depending on the overall composition of the peptide, the temperature, and the solvation conditions. This makes the system an interesting case to study the ensembles of peptide conformations as a function of temperature by MD simulation. Simulations involving the folding and unfolding of the peptide were performed starting from two initial structures, a right-handed alpha-helical structure and an extended structure, at three temperatures, 298 K, 340 K, and 380 K, and the results are compared with experimental nuclear magnetic resonance (NMR) data measured at 298 K and 340 K. The simulations generally reproduce the available experimental nuclear Overhauser effect (NOE) data, even when a wide range of conformations is sampled at each temperature. The importance of adequate statistical sampling in order to reliably interpret the experimental data is discussed.     

Structure of guanosine-3',5'-cytidine monophosphate. I. Semi-empirical potential energy calculations and model-building

The conformation and packing scheme for guanosine-3′, 5′-cytidine monophosphate, GpC, were computed by minimizing the classical potential energy. The lowest energy conformation of the isolated molecule had dihedral angles in the range of helical RNA's and the sugar pucker was C3′ endo. This was used as the starting conformation in a packing search over orientation space, the dihedral angles being flexible in this step also. The packing search was restricted by constraints from our x-ray data, namely, (1) the dimensions of the monoclinic unit cell and its pseudo-C2 symmetry (the real space group is P2₁), (2) the location of the phosphorous atom, and (3) the orientation of the bases. In addition, a geometric function was devised to impose Watson-Crick base pairing. Thus, a trial structure could be sought without explicit inclusion of intermolecular potentials. An interactive computer graphics system was used for visualizing the calculated structures. The packing searches yielded two lowest energy schemes in which the molecules had the same conformation (similar to double-helical RNA) but different orientations within the unit cell. One of these was refined by standard x-ray methods to a discrepancy index of 14.4% in the C2 pseudocell. This served as the starting structure for the subsequent refinement in the real P2₁ cell.⁵     

A comparison of the CHARMM, AMBER and ECEPP potentials for peptides. I. Conformational predictions for the tandemly repeated peptide (Asn-Ala-Asn-Pro)9

A search for low-energy helical and near-helical conformations of the tandemly repeated peptide (Asn-Ala-Asn-Pro)9 was undertaken by minimization of the CHARMM potential energy function from eight starting conformations; the latter were obtained from the two low-energy conformations of this repeated peptide found by Gibson & Scheraga, Proc. Natl. Acad. Sci. USA 83, 5649-5653 (1986), and the single conformation found by Brooks et al., Proc. Natl. Acad. Sci. USA 84, 4470-4474 (1987), and from modifications of these three conformations. The same eight starting conformations, as determined by dihedral angles, were used for minimizations of the AMBER and ECEPP potentials. Comparison of the final conformations by least-squares superposition of their C alpha atoms, and by inspection of the parameters of the ideal helix or coiled coil that most closely matched the coordinates of their C alpha atoms in a least-squares sense, showed that: (1) energy minimization, starting from the same conformation but using any two different potentials, could lead to final conformations whose resemblance to each other varied from acceptable to highly unsatisfactory; (2) the ordering of the final energy-minimized conformations, and the energy differences between them, were quite different for all three potentials; (3) the extent of agreement or disagreement between pairs of conformations generated using CHARMM and AMBER, CHARMM and ECEPP, or AMBER and ECEPP, respectively, was not significantly different. The lowest-energy conformation generated using each of the potentials was a left-handed helix, whose pitch and number of residues per turn were similar to those of the left-handed helix found by Gibson & Scheraga. Although the starting conformation which led to the lowest-energy conformation was different for all three potentials, pairwise superposition of the C alpha atoms in the final conformations showed root-mean-square deviations of only 1.0-1.3 A. It is concluded that energy minimizations starting from a large enough sample of initial conformations might on occasion lead to essentially the same conformational prediction whichever potential is used; however, if the sample of starting points is small, predictions based on the three potentials will usually diverge.     

Folding of a DNA hairpin loop structure in explicit solvent using replica-exchange molecular dynamics simulations

Hairpin loop structures are common motifs in folded nucleic acids. The 5'-GCGCAGC sequence in DNA forms a characteristic and stable trinucleotide hairpin loop flanked by a two basepair stem helix. To better understand the structure formation of this hairpin loop motif in atomic detail, we employed replica-exchange molecular dynamics (RexMD) simulations starting from a single-stranded DNA conformation. In two independent 36 ns RexMD simulations, conformations in very close agreement with the experimental hairpin structure were sampled as dominant conformations (lowest free energy state) during the final phase of the RexMDs ( approximately 35% at the lowest temperature replica). Simultaneous compaction and accumulation of folded structures were observed. Comparison of the GCA trinucleotides from early stages of the simulations with the folded topology indicated a variety of central loop conformations, but arrangements close to experiment that are sampled before the fully folded structure also appeared. Most of these intermediates included a stacking of the C(2) and G(3) bases, which was further stabilized by hydrogen bonding to the A(5) base and a strongly bound water molecule bridging the C(2) and A(5) in the DNA minor groove. The simulations suggest a folding mechanism where these intermediates can rapidly proceed toward the fully folded hairpin and emphasize the importance of loop and stem nucleotide interactions for hairpin folding. In one simulation, a loop motif with G(3) in syn conformation (dihedral flip at N-glycosidic bond) accumulated, resulting in a misfolded hairpin. Such conformations may correspond to long-lived trapped states that have been postulated to account for the folding kinetics of nucleic acid hairpins that are slower than expected for a semiflexible polymer of the same size.     

Exploring the energy landscape of protein folding using replica-exchange and conventional molecular dynamics simulations

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.     

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.     

Conformational study of a nine residue fragment of the antigenic loop of foot-and-mouth disease virus.

The nine-residue peptide Ac-TASARGDLA-NHMe was selected as model peptide in order to understand the conformational features of the antigenic loop of foot-and-mouth disease virus (FMDV). A throughout exploration of the conformational space has been carried out by means of molecular dynamics (MD) and energy minimization. The calculations have been carried out using the AMBER force field. Solvent effects have been included by an effective dielectric constant of epsilon = 4r. The lowest energy conformation presents a secondary structure constituted by an alpha-helix at the N-terminal end followed by two gamma-turns in the central region. The rest of the accessible minima found present also a high tendency to form gamma-turns. Finally, a 100 ps MD trajectory calculation at 298 K suggest a stability of the secondary structure elements of the lowest energy conformation.     

Development and testing of protocols for computer-aided design of peptide drugs, using oxytocin

Considerable clinical interest in neuropeptides and peptide hormones has stimulated recent research and development of peptide-based drugs. This process differs from most classical drug discovery procedures because peptide molecules have considerable inherent flexibility. In the present paper, to identify lowest energy and metastable conformers for drug design, and to develop protocols for such studies, conformational search algorithms, incorporating empirical energy calculations, have been applied in the analysis of the peptide oxytocin. Energy minimization in torsion angle space was carried out from a variety of starting conformations, including published structures, in all-atom mode and all with distance constraints for disulphide bond formation. The energy-minimized conformations have been further optimized by a mapping method. Complementary simulations have been performed in united-atom mode and a model representing the effects of water using dummy sites has been developed and tested for this representation. Several of the preferred conformers together with de novo conformations have been used as starting points in molecular dynamics simulations; 28 low potential energy conformations were located at a temperature of 4 K. Conformations are analysed to identify hydrogen bonds, phi-psi angle distributions and the RMS values relative to the X-ray structure of deamino-oxytocin. The modelled structure of lowest energy in the molecular mechanics calculations was also that of least RMS deviation from the crystal structure; whilst structures of lower energy but larger deviation were identified by molecular dynamics techniques. A metastable structure has been identified which satisfies existing criteria for the "active form", and this model is tested by a theoretical residue-substitution technique, to provide clues on the agonist/antagonist relationship at the atomic level.     

Folding-unfolding thermodynamics of a beta-heptapeptide from equilibrium simulations

The thermodynamics of folding and unfolding of a beta-heptapeptide in methanol solution has been studied at four different temperatures, 298 K, 340 K, 350 K, and 360 K, by molecular dynamics simulation. At each of these temperatures, the 50-ns simulations were sufficient to generate an equilibrium distribution between a relatively small number of conformations (approximately 10(2)), showing that, even above the melting temperature (approximately 340 K), the peptide does not randomly sample conformational space. The free energy of folding and the free energy difference between pairs of conformations have been calculated from their relative populations. The experimentally determined folded conformation at 298 K, a left-handed 3(1)-helix, is at each of the four temperatures the predominant conformation, with its probability and average lifetime decreasing with increasing temperature. The most common intermediates of folding and unfolding are also the same at the four temperatures. Paths and rates of interconversion between different conformations have been determined. It has been found that folding can occur through multiple pathways, not necessarily downhill in free energy, although the final step involves a reduced number of intermediates.     

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.     

The loop problem in proteins: A monte carlo simulated annealing approach

A Monte Carlo simulated annealing (MCSA) algorithm was used to generate the conformations of local regions in bovine pancreatic trypsin inhibitor (BPTI) starting from random initial conformations. In the approach explored, only the conformation of the segment is computed; the rest of the protein is fixed in the known native conformation. Rather than follow a single simulation exhaustively, computer time is better used by performing multiple independent MCSA simulations in which different starting temperatures are employed and the number of conformations sampled is varied. The best computed conformation is chosen on the basis of lowest total energy and refined further. The total energy used in the annealing is the sum of the intrasegment energy, the interaction energy of the segment with the local surrounding region, and a distance constraint to generate a smooth connection of the initially randomized segment with the rest of the protein. The rms deviations between the main-chain conformations of the computed segments in BPTI and those of the native x-ray structure are 0.94 Å for a 5-residue α-helical segment, 1.11 Å for a 5-residue β-strand segment, and 1.03, 1.61, and 1.87 Ã for 5-, 7-, and 9-residue loop segments. Side-chain deviations are comparable to the main-chain deviations for those side chains that interact strongly with the fixed part of the protein. A detailed view of the deviations at an atom-resolved level is obtained by comparing the predicted segments with their known conformations in the crystal structure of BPTI. These results emphasize the value of predetermined fixed structure against which the computed segment can nest. © 1993 John Wiley & Sons, Inc.     

Molecular dynamic simulations of environment and sequence dependent DNA conformations: the development of the BMS nucleic acid force field and comparison with experimental results

Molecular dynamic (MD) simulations using the BMS nucleic acid force field produce environment and sequence dependent DNA conformations that closely mimic experimentally derived structures. The parameters were initially developed to reproduce the potential energy surface, as defined by quantum mechanics, for a set of small molecules that can be used as the building blocks for nucleic acid macromolecules (dimethyl phosphate, cyclopentane, tetrahydrofuran, etc.). Then the dihedral parameters were fine tuned using a series of condensed phase MD simulations of DNA and RNA (in zero added salt, 4M NaCl, and 75% ethanol solutions). In the tuning process the free energy surface for each dihedral was derived from the MD ensemble and fitted to the conformational distributions and populations observed in 87 A- and B-DNA x-ray and 17 B-DNA NMR structures. Over 41 nanoseconds of MD simulations are presented which demonstrate that the force field is capable of producing stable trajectories, in the correct environments, of A-DNA, double stranded A-form RNA, B-DNA, Z-DNA, and a netropsin-DNA complex that closely reproduce the experimentally determined and/or canonical DNA conformations. Frequently the MD averaged structure is closer to the experimentally determined structure than to the canonical DNA conformation. MD simulations of A- to B- and B- to A-DNA transitions are also shown. A-DNA simulations in a low salt environment cleanly convert into the B-DNA conformation and converge into the RMS space sampled by a low salt simulation of the same sequence starting from B-DNA. In MD simulations using the BMS force field the B-form of d(GGGCCC)2 in a 75% ethanol solution converts into the A-form. Using the same methodology, parameters, and conditions the A-form of d(AAATTT)2 correctly converts into the B-DNA conformation. These studies demonstrate that the force field is capable of reproducing both environment and sequence dependent DNA structures. The 41 nanoseconds (nsec) of MD simulations presented in this paper paint a global picture which suggests that the DNA structures observed in low salt solutions are largely due to the favorable internal energy brought about by the nearly uniform screening of the DNA electrostatics. While the conformations sampled in high salt or mixed solvent environments occur from selective and asymmetric screening of the phosphate groups and DNA grooves, respectively, brought about by sequence induced ion and solvent packing.     

Ab initio structure prediction for small polypeptides and protein fragments using genetic algorithms

Ab initio folding simulations have been performed on three peptides, using a genetic algorithm-based search method which operates on a full atom representation. Conformations are evaluated with an empirical force field parameterized by a potential of mean force analysis of experimental structures. The dominant terms in the force field are local and nonlocal main chain electrostatics and the hydrophobic effect. Two of the simulated structures were for fragments of complete proteins (eosinophil-derived neurotoxin (EDN) and the subtilisin propeptide) that were identified as being likely initiation sites for folding. The experimental structure of one of these (EDN) was subsequently found to be consistent with that prediction (using local hydrophobic burial as the determinant for independent folding). The simulations of the structures of these two peptides were only partly successful. The most successful folding simulation was that of a 22-residue peptide corresponding to the membrane binding domain of blood coagulation factor VIII (Membind). Three simulations were performed on this peptide and the lowest energy conformation was found to be the most similar to the experimental structure. The conformation of this peptide was determined with a C_α rms deviation of 4.4 Å. Although these simulations were partly successful there are still many unresolved problems, which we expect to be able to address in the next structure prediction experiment. © 1995 Wiley-Liss, Inc.     

Dipeptide backbone conformation and antibody recognition of a viral octapeptide epitope.

The peptide YKGTMDSG (Tyr-Lys-Gly-Thr-Met-Asp-Ser-Gly) represents an important antigenic determinant from the glycoprotein G2 of the pathogenic Rift Valley fever virus. By preparing a series of single-residue substitution peptides, the importance to antigenicity of individual residues within this octapeptide has been determined. Here, we investigated a simple and rapid computational analysis to test for correlations between the observed antigenicity of the substitution analogue peptides and the calculated conformational preferences in local regions of the peptides. Conformational energy analyses were carried out on all dipeptide combinations represented in the wild-type octapeptide and in the single-residue substitution analogue peptides. Conformational similarities and differences between wild-type and substitution dipeptide pairs were determined. The results of these computational analyses were then compared with the data on the relative antigenicity of the wild-type octapeptide and the substitution analogues. This comparison revealed a positive correlation. Substitution peptides showing changes in antigenicity possessed significant changes in the calculated backbone conformation relative to wild type in the dipeptides encompassing the residue substitution. Substitution peptides showing no change in antigenicity similarly showed no significant changes in dipeptide conformation. The potential utility of dipeptide conformational energy analyses and this preliminary structure-activity correlation are discussed.     

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.     

Conformational Dynamics of a Ligand-Free Adenylate Kinase

Adenylate kinase (AdK) is a phosphoryl-transfer enzyme with important physiological functions. Based on a ligand-free open structure and a ligand-bound closed structure solved by crystallography, here we use molecular dynamics simulations to examine the stability and dynamics of AdK conformations in the absence of ligands. We first perform multiple simulations starting from the open or the closed structure, and observe their free evolutions during a simulation time of 100 or 200 nanoseconds. In all seven simulations starting from the open structure, AdK remained stable near the initial conformation. The eight simulations initiated from the closed structure, in contrast, exhibited large variation in the subsequent evolutions, with most (seven) undergoing large-scale spontaneous conformational changes and approaching or reaching the open state. To characterize the thermodynamics of the transition, we propose and apply a new sampling method that employs a series of restrained simulations to calculate a one-dimensional free energy along a curved pathway in the high-dimensional conformational space. Our calculated free energy profile features a single minimum at the open conformation, and indicates that the closed state, with a high (∼13 kcal/mol) free energy, is not metastable, consistent with the observed behaviors of the unrestrained simulations. Collectively, our simulations suggest that it is energetically unfavorable for the ligand-free AdK to access the closed conformation, and imply that ligand binding may precede the closure of the enzyme.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.