All-Atom Monte Carlo Approach to Protein-Peptide Binding

We develop a procedure for exploring the free energy landscape of protein-peptide binding at atomic detail and apply it to PDZ domain-peptide interactions. The procedure involves soft constraints on receptor proteins providing limited chain flexibility, including backbone motions. Peptide chains are left fully flexible and kept in spatial proximity of the protein through periodic boundary conditions. By extensive Monte Carlo simulations, full representative conformational ensembles at temperatures where bound and unbound states coexist are obtained. To make this approach computationally feasible, we develop an effective all-atom energy function centering on hydrophobicity, hydrogen bonding, and electrostatic interactions. Our initial focus is a set of 11 PDZ domain-peptide pairs with experimentally determined complex structures. Minimum-energy conformations are found to be highly similar to the respective native structures in eight of the cases (all-atom peptide RMSDs < 6 Å). Having achieved that, we turn to a more complete characterization of the bound peptide state through a clustering scheme applied on the full ensembles of peptide structures. We find a significant diversity among bound peptide conformations for several PDZ domains, in particular involving the N terminal side of the peptide chains. Our computational model is then tested further on a set of nine PDZ domain-peptide pairs where the peptides are not originally present in the experimentally determined structures. We find a similar success rate in terms of the nativeness of minimum-energy conformations. Finally, we investigate the ability of our approach to capture variations in binding affinities for different peptide sequences. This is done in particular for a set of related sequences binding to the third PDZ domain of PSD-95 with encouraging results.     

De novo prediction of polypeptide conformations using dihedral probability grid Monte Carlo methodology.

We tested the dihedral probability grid Monte Carlo (DPG-MC) methodology to determine optimal conformations of polypeptides by applying it to predict the low energy ensemble for two peptides whose solution NMR structures are known: integrin receptor peptide (YGRGDSP, Type II beta-turn) and S3 alpha-helical peptide (YMSEDEL KAAEAAFKRHGPT). DPG-MC involves importance sampling, local random stepping in the vicinity of a current local minima, and Metropolis sampling criteria for acceptance or rejection of new structures. Internal coordinate values are based on side-chain-specific dihedral angle probability distributions (from analysis of high-resolution protein crystal structures). Important features of DPG-MC are: (1) Each DPG-MC step selects the torsion angles (phi, psi, chi) from a discrete grid that are then applied directly to the structure. The torsion angle increments can be taken as S = 60, 30, 15, 10, or 5 degrees, depending on the application. (2) DPG-MC utilizes a temperature-dependent probability function (P) in conjunction with Metropolis sampling to accept or reject new structures. For each peptide, we found close agreement with the known structure for the low energy conformational ensemble located with DPG-MC. This suggests that DPG-MC will be useful for predicting conformations of other polypeptides.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

Exploring the free energy landscape of a model β‐hairpin peptide and its isoform

Secondary structural transitions from α‐helix to β‐sheet conformations are observed in several misfolding diseases including Alzheimer's and Parkinson's. Determining factors contributing favorably to the formation of each of these secondary structures is therefore essential to better understand these disease states. β‐hairpin peptides form basic components of anti‐parallel β‐sheets and are suitable model systems for characterizing the fundamental forces stabilizing β‐sheets in fibrillar structures. In this study, we explore the free energy landscape of the model β‐hairpin peptide GB1 and its E2 isoform that preferentially adopts α‐helical conformations at ambient conditions. Umbrella sampling simulations using all‐atom models and explicit solvent are performed over a large range of end‐to‐end distances. Our results show the strong preference of GB1 and the E2 isoform for β‐hairpin and α‐helical conformations, respectively, consistent with previous studies. We show that the unfolded states of GB1 are largely populated by misfolded β‐hairpin structures which differ from each other in the position of the β‐turn. We discuss the energetic factors contributing favorably to the formation of α‐helix and β‐hairpin conformations in these peptides and highlight the energetic role of hydrogen bonds and non‐bonded interactions. Proteins 2014; 82:2394–2402. © 2014 Wiley Periodicals, Inc.     

Monte Carlo studies of folding, dynamics, and stability in alpha-helices

Folding simulations of polyalanine peptides were carried out using an off-lattice Monte Carlo simulation technique. The peptide was represented as a chain of residues, each of which contains two interaction sites: one corresponding to the C(alpha) atom and the other to the side chain. A statistical potential was used to describe the interaction between these sites. The preferred conformations of the peptide chain on the energy surface, starting from several initial conditions, were searched by perturbations on its generalized coordinates with the Metropolis criterion. We observed that, at low temperatures, the effective energy was low and the helix content high. The calculated helix propagation (s) and nucleation (sigma) parameters of the Zimm-Bragg model were in reasonable agreement with the empirical data. Exploration of the energy surface of the alanine-based peptides (AAQAA)(3) and AAAAA(AAARA)(3)A demonstrated that their behavior is similar to that of polyalanine, in regard to their effective energy, helix content, and the temperature-dependence of their helicity. In contrast, stable secondary structures were not observed for (Gly)(20) at similar temperatures, which is consistent with the nonfolder nature of this peptide. The fluctuations in the slowest dynamics mode, which describe the elastic behavior of the chain, showed that as the temperature decreases, the polyalanine peptides become stiffer and retain conformations with higher helix content. Clustering of conformations during the folding phase implied that polyalanine folds into a helix through fewer numbers of intermediate conformations as the temperature decreases.     

Stereochemical studies on cyclic peptides: Detailed energy minimization studies on hydrogen bonded all-trans cyclic pentapeptide backbones

Conformational studies have been carried out on hydrogenbonded all-trans cyclic pentapeptide backbone. Application of a combination of grid search and energy minimization on this system has resulted in obtaining 23 minimum energy conformations, which are characterized by unique patterns of hydrogen bonding comprising of β- and γ-turns. A study of the minimum energy conformationsvis-a-vis non-planar deviation of the peptide units reveals that non-planarity is an inherent feature in many cases. A study on conformational clustering of minimum energy conformations shows that the minimum energy conformations fall into 6 distinct conformational families. Preliminary comparison with available X-ray structures of cyclic pentapeptide indicates that only some of the minimum energy conformations have formed crystal structures. The set of minimum energy conformations worked out in the present study can form a consolidated database of prototypes for hydrogen bonded backbone and be useful for modelling cyclic pentapeptides both synthetic and bioactive in nature. This is part XV of the series. Part XIV in this series is Ramakrishnanet al 1987.     

Free energy landscapes of two model peptides: α-helical and β-hairpin peptides explored with Brownian dynamics simulation

We applied an atomistic Brownian dynamics (BD) simulation with multiple time step method for the folding simulation of a 13-mer α-helical peptide and a 12-mer β-hairpin peptide, giving successful folding simulations. In this model, the driving energy contribution towards folding came from both electrostatic and van der Waals interactions for the α-helical peptide and from van der Waals interactions for the β-hairpin peptide. Although, many non-native structures having the same or lower energy than that of native structure were observed, the folded states formed the most populated cluster when the structures obtained by the BD simulations were subjected to the cluster analysis based on distance-based root mean square deviation of side-chains between different structures. This result indicates that we can predict the native structures from conformations sampled by BD simulation.     

Conformational analysis of the 20-residue membrane-bound portion of melittin by conformational space annealing

The conformational space of the 20-residue membrane-bound portion of melittin has been investigated extensively with the conformational space annealing (CSA) method and the ECEPP/3 (Empirical Conformational Energy Program for Peptides) algorithm. Starting from random conformations, the CSA method finds that there are at least five different classes of conformations, within 4 kcal/mol, which have distinct backbone structures. We find that the lowest energy conformation of this peptide from previous investigations is not the global minimum-energy conformation (GMEC); but it belongs to the second lowest energy class of the five classes found here. In four independent runs, one conformation is found repeatedly as the lowest energy conformation of the peptide (two of the four lowest energy conformations are identical; the other two have essentially identical backbone conformations but slightly different side-chain conformations). We propose this conformation, whose energy is lower than that found previously by 1.9 kcal/mol, as the GMEC of the ECEPP/3 force field. The structure of the proposed GMEC is less helical and more compact than the previous one. It appears that the CSA method can find several classes of conformations of a 20-residue peptide starting from random conformations utilizing only its amino acid sequence information. The proposed GMEC has also been found with a modified electrostatically driven Monte Carlo method [D. R. Ripoll, A. Liwo, and H.A. Scheraga (1998) “New Developments of the Electrostatically Driven Monte Carlo Method: Test on the Membrane-Bound Portion of Melittin,” Biopolymers, Vol. 46, pp. 117–126]. © 1998 John Wiley & Sons, Inc. Biopoly 46: 103–115, 1998     

Molecular dynamics simulation of a leucine zipper motif predicted for the integrase of human immunodeficiency virus type I

We have used the molecular dynamics (MD) simulation package AMBER4 to search the conformation of a peptide predicted as a leucine zipper motif for the human immunodeficiency virus type I integrase protein (HIV IN-LZM). The peptide is composed of 22 amino acid residues and its location is from Val 151 to Leu 172. The searching procedure also includes two known α-helices that served as positive controls—namely, a 22-residue GCN4-p1 (LZM) and a 20-residue poly(L -alanine) (PLA). A 21-residue peptide extracted from a cytochrome C crystal (CCC-t) with determined conformation as a β-turn is also included as a negative control. At the beginning of the search, two starting conformations—namely, the standard right-handed α-helix and the fully stretched conformations—are generated for each peptide. Structures generated as standard α-helix are equilibrated at room temperature for 90 ps while structures generated as a fully stretched one are equilibrated at 600 K for 120 ps. The CCC-t and PLA helices are nearly destroyed from the beginning of equilibration. However, for both the HIV IN-LZM and the GCN4-p1 LZM structures, there is substantial helicity being retained throughout the entire course of equilibration. Although helix propagation profiles calculated indicate that both peptides possess about the same propensity to form an α-helix, the HIV IN-LZM helix appears to be more stable than the GCN4-p1 one as judged by a variety of analyses on both structures generated during the equilibration course. The fact that predicted HIV IN-LZM can exist as an α-helix is also supported by the results of high temperature equilibration run on the fully stretched structures generated. In this run, the RMS deviations between the backbone atoms of the structures with the lowest potential energy (PE) identified within every 2 ps and the structure with the lowest PE searched in the same course of simulation are calculated. For both the HIV IN-LZM and the GCN4-p1 LZM, these rms values decrease with the decrease of PE, which indicates that both structures are closer in conformations as their PEs are moved deeper into the PE well. © 1994 John Wiley & Sons, Inc.     

Theoretical conformational analysis of a encephalitogenic peptide molecule and a study of the structure-activity relationship in a series of its analogs

Semi-empirical energy calculations are used to determine all low-energy conformations of Trp-containing fragment 113-121 of myelin basic protein (experimental allergic encephalomyelitis inducing peptide). The computed conformations are compared with the results of physico-chemical experiments and data on biological testing of the encephalitogenic peptide analogs. The three computed structures are shown to be in a good agreement with the available experimental evidence. However, additional information is required to predict "biologically active" conformation of encephalitogenic peptide.     

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.     

Energy-conformation studies of frequency of beta-turns in tetrapeptide sequences

The optimized energies of seven beta-bends, repeating C5 and C7, and right- and left-handed alpha-helical conformations for each of eight tetrapeptides have been computed using empirical methods. Eight tetramers were selected: four helix-forming sequences with hydrophobic residues such as Val, Leu, Ile and Trp, and four helix-breaking sequences with hydrophilic residues such as Asp, Asn and Ser, as determined by their frequency of occurrence in beta turns in proteins. Analysis of the optimized conformations with energies less than or equal to 2.1 kcal/mol from the absolute minimum energy conformer for each tetramer reveals a correlation between low-energy conformations and those predicted from observed protein structures. These results show that energy calculations on small peptide fragments may be usefulin predicting protein structure.     

Lipid Tail Protrusion in Simulations Predicts Fusogenic Activity of Influenza Fusion Peptide Mutants and Conformational Models

Fusion peptides from influenza hemagglutinin act on membranes to promote membrane fusion, but the mechanism by which they do so remains unknown. Recent theoretical work has suggested that contact of protruding lipid tails may be an important feature of the transition state for membrane fusion. If this is so, then influenza fusion peptides would be expected to promote tail protrusion in proportion to the ability of the corresponding full-length hemagglutinin to drive lipid mixing in fusion assays. We have performed molecular dynamics simulations of influenza fusion peptides in lipid bilayers, comparing the X-31 influenza strain against a series of N-terminal mutants. As hypothesized, the probability of lipid tail protrusion correlates well with the lipid mixing rate induced by each mutant. This supports the conclusion that tail protrusion is important to the transition state for fusion. Furthermore, it suggests that tail protrusion can be used to examine how fusion peptides might interact with membranes to promote fusion. Previous models for native influenza fusion peptide structure in membranes include a kinked helix, a straight helix, and a helical hairpin. Our simulations visit each of these conformations. Thus, the free energy differences between each are likely low enough that specifics of the membrane environment and peptide construct may be sufficient to modulate the equilibrium between them. However, the kinked helix promotes lipid tail protrusion in our simulations much more strongly than the other two structures. We therefore predict that the kinked helix is the most fusogenic of these three conformations.     

Computational and experimental determination of the alpha-helix unfolding reaction coordinate

We demonstrate a calculated alpha-helix peptide folding energy landscape which accurately simulates the first experimentally measured alpha-helix melting energy landscape. We examine a 21-amino acid, mainly polyalanine peptide and calculate the free energy along the Psi Ramachandran angle secondary folding coordinate. The experimental free energy landscape was determined using UV resonance Raman spectroscopy. The relative free energy values are very close as are the equilibrium peptide conformations. We find 2.3 kcal/mol activation barriers between the alpha-helix-like and PPII-like basins. We also find that the alpha-helix-like conformations are quite defective and the alpha-helix-like structure dynamically samples 310-helix and pi-bulges.     

Refinement of the thrombin-bound structure of a hirudin peptide by a restrained electrostatically driven Monte Carlo method.

Energy refinement of the structure of a linear peptide, hirudin56-65, bound to thrombin was carried out using a conformational search method in combination with restrained minimization. Five conformations originated from nmr data and distance geometry calculations having a similar global folding pattern but quite different backbone conformations were used as the starting structures. As a result of this approach, a series of low-energy conformations compatible with a set of upper and lower bounds of interproton distances determined from transferred nuclear Overhauser effects were found. A comparison among the lowest energy conformations of each run showed that the combination of energy refinement plus distance constraints led to a very well-defined structure for both the backbone and the side chains of the last 7 residues of the polypeptide. Furthermore, the low-energy conformations generated with this technique contain a segment of 3(10)-helix involving the last 5 residues at the COOH terminal end.     

Influence of solvent molecules on the stereochemical code of glycyl residues in proteins

The Ramachandran steric map and energy diagrams of the glycyl residue are symmetric. A plot of (phi,psi) angles of glycyl residues in 250 nonhomologous and high-resolution protein structures is also largely symmetric. However, there is a clear aberration in the symmetry. Although there is a cluster of points corresponding to the right-handed alpha-helical region, the "equivalent" cluster is clearly shifted to in and around the (phi,psi) values of (90 degrees, 0 degrees ) instead of being centered at the left-handed alpha-helical region of (60 degrees, 40 degrees ). This lack of symmetry exists even in the (phi,psi) distribution of residues from non-alpha-helical regions in proteins. Here we provide an explanation for this observation. An analysis of glycyl conformations in small peptide structures and in "coil" proteins, which are largely devoid of helical and sheet regions, shows that glycyl residues prefer to adopt conformations around (+/-90 degrees, 0 degrees ) instead of right- and left-handed alpha-helical regions. By using theoretical calculations, such conformations are shown to have highest solvent accessibility in a system of two-linked peptide units with glycyl residue at the central C(alpha) atom. This finding is consistent with the observations from 250 nonhomologous protein structures where glycyl residues with conformations close to (+/-90 degrees, 0 degrees ) are seen to have high solvent accessibility. Analysis of a subset of nonhomologous structures with very high resolution (1.5 A or better) shows that water molecules are indeed present at distances suitable for hydrogen bond interaction with glycyl residues possessing conformations close to (+/-90 degrees, 0 degrees ). It is suggested that water molecules play a key role in determining and stabilizing these conformations of glycyl residues and explain the aberration in the symmetry of glycyl conformations in proteins.     

UV resonance Raman investigation of a 3(10)-helical peptide reveals a rough energy landscape

We used UVRRS at 194 and 204 nm excitation to examine the backbone conformation of a 13-residue polypeptide (gp41(659-671)) that has been shown by NMR to predominantly fold into a 3(10)-helix. Examination of the conformation sensitive AmIII(3) region indicates the peptide has significant populations of beta-turn, PPII, 3(10)-helix, and pi-helix-like conformations but little alpha-helix. We estimate that at 1 degree C on average six of the 12 peptide bonds are in folded conformations (predominantly 3(10)- and pi-helix), while the other six are in unfolded (beta-turn/PPII) conformations. The folded and unfolded populations do not change significantly as the temperature is increased from 1 to 60 degrees C, suggesting a unique energy landscape where the folded and unfolded conformations are essentially degenerate in energy and exhibit identical temperature dependences.     

Enhanced sampling of the molecular potential energy surface using mutually orthogonal latin squares: application to peptide structures

The computational identification of the optimal three-dimensional fold of even a small peptide chain from its sequence, without reference to other known structures, is a complex problem. There have been several attempts at solving this by sampling the potential energy surface of the molecule in a systematic manner. Here we present a new method to carry out the sampling, and to identify low energy conformers of the molecule. The method uses mutually orthogonal Latin squares to select (of the order of) n(2) points from the multidimensional conformation space of size m(n), where n is the number of dimensions (i.e., the number of conformational variables), and m specifies the fineness of the search grid. The sampling is accomplished by first calculating the value of the potential energy function at each one of the selected points. This is followed by analysis of these values of the potential energy to obtain the optimal value for each of the n-variables separately. We show that the set of the n-optimal values obtained in this manner specifies a low energy conformation of the molecule. Repeated application of the method identifies other low energy structures. The computational complexity of this algorithm scales as the fourth power of the size of the molecule. We applied this method to several small peptides, such as the neuropeptide enkephalin, and could identify a set of low energy conformations for each. Many of the structures identified by this method have also been previously identified and characterized by experiment and theory. We also compared the best structures obtained for the tripeptide (Ala)(3) by the present method, with those obtained by an exhaustive grid search, and showed that the algorithm is successful in identifying all the low energy conformers of this molecule.     

Molecular dynamics study of disulfide bond influence on properties of an RGD peptide.

Three 1 ns length molecular dynamics simulations of an RGD peptide (Ac-Pen-Arg-Gly-Asp-Cys-NH2, with Pen denoting penicillamine) have been performed in aqueous solution, one for the disulfide bridged, and two for the unbridged form. The trajectories were analyzed to identify conformations explored by the two forms and to calculate several properties: NMR vicinal coupling constants, order parameters, dipole moments and diffusion coefficients, in an effort to describe the physical role of the disulfide bond. The cyclic peptide was able to explore several distinct backbone conformations centered around a turn-extended-turn structure. However, its flexibility was limited and it appeared to be 'locked in' into a a family of structures characterized by a high dipole moment and a well-defined conformation of the pharmacophore, which has been previously identified as biologically active. Excellent agreement between the simulated and observed NMR vicinal coupling constants indicates that realistic structures were sampled in the cyclic peptide simulation. The linear form of the peptide was much more flexible than the cyclic one. In the two independent 1 ns simulations of the linear form the explored conformations could be roughly grouped into two classes, of cyclic-like and extended type. Within each simulation the peptide switched between the two classes of structures several times. Exact matches between conformations in the two linear peptide simulations were not found; several conformational regions with backbone rms deviations below 1A were identified, suggesting that representative structures of the linear form have also been identified. In the linear peptide simulations the RGD pharmacophore is able to adopt a wide range of conformations, including the one preferred by the cyclic form. The lower biological activity of the linear peptide compared to the cyclic one may be correlated with the lower population of this structure in the absence of the disulfide bond.     

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.