Spontaneous beta-barrel formation: an all-atom Monte Carlo study of Abeta16-22 oligomerization

Using all-atom Monte Carlo simulations with implicit water, combined with a cluster size analysis, we study the aggregation of Abeta(16) (-22), a peptide capable of forming amyloid fibrils. We consider a system of six initially randomly oriented Abeta(16) (-22) peptides, and investigate the thermodynamics and structural properties of aggregates formed by this system. The system is unaggregated without ordered secondary structure at high temperature, and forms beta-sheet rich aggregates at low temperature. At the crossover between these two regimes, we find that clusters of all sizes occur, whereas the beta-strand content is low. In one of several runs, we observe the spontaneous formation of a beta-barrel with six antiparallel strands. The beta-barrel stands out as the by far most long-lived aggregate seen in our simulations.     

Toward minimalist models of larger proteins: a ubiquitin-like protein

Our recently developed off-lattice bead model capable of simulating protein structures with mixed alpha/beta content has been extended to model the folding of a ubiquitin-like protein and provides a means for examining the more complex kinetics involved in the folding of larger proteins. Using trajectories generated from constant-temperature Langevin dynamics simulations and sampling with the multiple multi-histogram method over five-order parameters, we are able to characterize the free energy landscape for folding and find evidence for folding through compact intermediates. Our model reproduces the observation that the C-terminus loop structure in ubiquitin is the last to fold in the folding process and most likely plays a spectator role in the folding kinetics. The possibility of a productive metastable intermediate along the folding pathway consisting of collapsed states with no secondary structure, and of intermediates or transition structures involving secondary structural elements occurring early in the sequence, is also supported by our model. The kinetics of folding remain multi-exponential below the folding temperature, with glass-like kinetics appearing at T/T(f) approximately 0.86. This new physicochemical model, designed to be predictive, helps validate the value of modeling protein folding at this level of detail for genomic-scale studies, and motivates further studies of other protein topologies and the impact of more complex energy functions, such as the addition of solvation forces.     

Free-energy landscape of the GB1 hairpin in all-atom explicit solvent simulations with different force fields: Similarities and differences

Although it is now possible to fold peptides and miniproteins in molecular dynamics simulations, it is well appreciated that force fields are not all transferable to different proteins. Here, we investigate the influence of the protein force field and the solvent model on the folding energy landscape of a prototypical two‐state folder, the GB1 hairpin. We use extensive replica‐exchange molecular dynamics simulations to characterize the free‐energy surface as a function of temperature. Most of these force fields appear similar at a global level, giving a fraction folded at 300 K between 0.2 and 0.8 in all cases, which is a difference in stability of 2.8 kT, and are generally consistent with experimental data at this temperature. The most significant differences appear in the unfolded state, where there are different residual secondary structures which are populated, and the overall dimensions of the unfolded states, which in most of the force fields are too collapsed relative to experimental Förster Resonance Energy Transfer (FRET) data. Proteins 2011. © 2010 Wiley‐Liss, Inc.     

Side-chain entropy effects on protein secondary structure formation

Loss of conformational entropy is one of the primary factors opposing protein folding. Both the backbone and side-chain of each residue in a protein will have their freedom of motion restricted in the final folded structure. The type of secondary structure of which a residue is part will have a significant impact on how much side-chain entropy is lost. Side-chain conformational entropies have previously been determined for folded proteins, simple models of unfolded proteins, alpha-helices, and a dipeptide model for beta-strands, but not for polyproline II (PII) helices. In this work, we present side-chain conformational estimates for the three regular secondary structure types: alpha-helices, beta-strands, and PII helices. Entropies are estimated from Monte Carlo computer simulations. Beta-strands are modeled as two structures, parallel and antiparallel beta-strands. Our data indicate that restraining a residue to the PII helix or antiparallel beta-strand conformations results in side-chain entropies equal to or higher than those obtained by restraining residues to the parallel beta-strand conformation. Side-chains in the alpha-helix conformation have the lowest side-chain entropies. The observation that extended structures retain the most side-chain entropy suggests that such structures would be entropically favored in unfolded proteins under folding conditions. Our data indicate that the PII helix conformation would be somewhat favored over beta-strand conformations, with antiparallel beta-strand favored over parallel. Notably, our data imply that, under some circumstances, residues may gain side-chain entropy upon folding. Implications of our findings for protein folding and unfolded states are discussed.     

Molecular dynamics study of a hyperthermophilic and a mesophilic rubredoxin

In recent years, increased interest in the origin of protein thermal stability has gained attention both for its possible role in understanding the forces governing the folding of a protein and for the design of new highly stable engineered biocatalysts. To study the origin of thermostability, we have performed molecular dynamics simulations of two rubredoxins, from the mesophile Clostridium pasteurianum and from the hyperthermophile Pyrococcus furiosus. The simulations were carried out at two temperatures, 300 and 373 K, for each molecule. The length of the simulations was within the range of 6-7.2 ns. The rubredoxin from the hyperthermophilic organism was more flexible than its mesophilic counterpart at both temperatures; however, the overall flexibility of both molecules at their optimal growth temperature was the same, despite 59% sequence homology. The conformational space sampled by both molecules was larger at 300 K than at 373 K. The essential dynamics analysis showed that the principal overall motions of the two molecules are significantly different. On the contrary, each molecule showed similar directions of motion at both temperatures.     

Thermal folding and mechanical unfolding pathways of protein secondary structures

Mechanical stretching of secondary structures is studied through molecular dynamics simulations of a Go-like model. Force versus displacement curves are studied as a function of the stiffness and velocity of the pulling device. The succession of stretching events, as measured by the order in which contacts are ruptured, is compared to the sequencing of events during thermal folding and unfolding. Opposite cross-correlations are found for an alpha-helix and a beta-hairpin structure. In a tandem of two alpha-helices, the two constituent helices unravel nearly simultaneously. A simple condition for simultaneous versus sequential unraveling of repeat units is presented.     

Folding and stability of the three-stranded beta-sheet peptide Betanova: insights from molecular dynamics simulations

The dynamics of the three-stranded beta-sheet peptide Betanova has been studied at four different temperatures (280, 300, 350, and 450 K by molecular dynamics simulation techniques, in explicit water. Two 20-ns simulations at 280 K indicate that the peptide remains very flexible under "folding" conditions sampling a range of conformations that together satisfy the nuclear magnetic resonance (NMR)-derived experimental constraints. Two simulations at 300 K (above the experimental folding temperature) of 20 ns each show partial formation of "native"-like structure, which also satisfies most of the NOE constraints at 280 K. At higher temperature, the presence of compact states, in which a series of hydrophobic contacts remain present, are observed. This is consistent with experimental observations regarding the role of hydrophobic contacts in determining the peptide's stability and in initiating the formation of turns and loops. A set of different structures is shown to satisfy NMR-derived distance restraints and a possible mechanism for the folding of the peptide into the NMR-determined structure is proposed.     

Sequence determinants of the capping box, a stabilizing motif at the N-termini of alpha-helices.

The capping box, a recurrent hydrogen bonded motif at the N-termini of alpha-helices, caps 2 of the initial 4 backbone amide hydrogen donors of the helix (Harper ET, Rose GD, 1993, Biochemistry 32:7605-7609). In detail, the side chain of the first helical residue forms a hydrogen bond with the backbone of the fourth helical residue and, reciprocally, the side chain of the fourth residue forms a hydrogen bond with the backbone of the first residue. We now enlarge the earlier definition of this motif to include an accompanying hydrophobic interaction between residues that bracket the capping box sequence on either side. The expanded box motif--in which 2 hydrogen bonds and a hydrophobic interaction are localized within 6 consecutive residues--resembles a glycine-based capping motif found at helix C-termini (Aurora R, Srinivasan R, Rose GD, 1994, Science 264:1126-1130).     

Elucidating protein secondary structures using alpha-carbon recurrence quantifications.

Secondary structures of proteins were studied by recurrence quantification analysis (RQA). High-resolution, 3-dimensional coordinates of alpha-carbon atoms comprising a set of 68 proteins were downloaded from the Protein Data Bank. By fine-tuning four recurrence parameters (radius, line, residue, separation), it was possible to establish excellent agreement between percent contribution of alpha-helix and beta-sheet structures determined independently by RQA and that of the DSSP algorithm (Define Secondary Structure of Proteins). These results indicate that there is an equivalency between these two techniques, which are based upon totally different pattern recognition strategies. RQA enhances qualitative contact maps by quantifying the arrangements of recurrent points of alpha carbons close in 3-dimensional space. For example, the radius was systematically increased, moving the analysis beyond local alpha-carbon neighborhoods in order to capture super-secondary and tertiary structures. However, differences between proteins could only be detected within distances up to about 6-11 A, but not higher. This result underscores the complexity of alpha-carbon spacing when super-secondary structures appear at larger distances. Finally, RQA-defined secondary structures were found to be robust against random displacement of alpha carbons upwards of 1 A. This finding has potential import for the dynamic functions of proteins in motion.     

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.     

A new residue-nucleotide propensity potential with structural information considered for discriminating protein-RNA docking decoys

Understanding the key factors that influence the preferences of residue-nucleotide interactions in specific protein-RNA interactions has remained a research focus. We propose an effective approach to derive residue-nucleotide propensity potentials through considering both the types of residues and nucleotides, and secondary structure information of proteins and RNAs from the currently largest nonredundant and nonribosomal protein-RNA interaction database. To test the validity of the potentials, we used them to select near-native structures from protein-RNA docking poses. The results show that considering secondary structure information, especially for RNAs, greatly improves the predictive power of pair potentials. The success rate is raised from 50.7 to 65.5% for the top 2000 structures, and the number of cases in which a near-native structure is ranked in top 50 is increased from 7 to 13 out of 17 cases. Furthermore, the exclusion of ribosomes from the database contributes 8.3% to the success rate. In addition, some very interesting findings follow: (i) the protein secondary structure element π-helix is strongly associated with RNA-binding sites; (ii) the nucleotide uracil occurs frequently in the most preferred pairs in which the unpaired and non-Watson-Crick paired uracils are predominant, which is probably significant in evolution. The new residue-nucleotide potentials can be helpful for the progress of protein-RNA docking methods, and for understanding the mechanisms of protein-RNA interactions.     

Analysis of interactive packing of secondary structural elements in alpha/beta units in proteins

An alpha-helix and a beta-strand are said to be interactively packed if at least one residue in each of the secondary structural elements loses 10% of its solvent accessible contact area on association with the other secondary structural element. An analysis of all such 5,975 nonidentical alpha/beta units in protein structures, defined at < or = 2.5 A resolution, shows that the interaxial distance between the alpha-helix and the beta-strand is linearly correlated with the residue-dependent function, log[(V/nda)/n-int], where V is the volume of amino acid residues in the packing interface, nda is the normalized difference in solvent accessible contact area of the residues in packed and unpacked secondary structural elements, and n-int is the number of residues in the packing interface. The beta-sheet unit (beta u), defined as a pair of adjacent parallel or antiparallel hydrogen-bonded beta-strands, packing with an alpha-helix shows a better correlation between the interaxial distance and log(V/nda) for the residues in the packing interface. This packing relationship is shown to be useful in the prediction of interaxial distances in alpha/beta units using the interacting residue information of equivalent alpha/beta units of homologous proteins. It is, therefore, of value in comparative modeling of protein structures.     

Protein secondary structure assignment through Voronoï tessellation

We present a new automatic algorithm, named VoTAP (Vo ronoï T essellation A ssignment P rocedure), which assigns secondary structures of a polypeptide chain using the list of α‐carbon coordinates. This program uses three‐dimensional Voronoï tessellation. This geometrical tool associates with each amino acid a Voronoï polyhedron, the faces of which unambiguously define contacts between residues. Thanks to the face area, for the contacts close together along the primary structure (low‐order contacts) a distinction is made between strong and normal ones. This new definition yields new contact matrices, which are analyzed and used to assign secondary structures. This assignment is performed in two stages. The first one uses contacts between residues close together along the primary structure and is based on data collected on a bank of 282 well‐refined nonredundant structures. In this bank, associations were made between the prints defined by these low‐order contacts and the assignments performed by different automatic methods. The second step focuses on the strand assignment and uses contacts between distant residues. Comparison with several other automatic assignment methods are presented, and the influence of resolution on the assignment is investigated. Proteins 2004. © 2004 Wiley‐Liss, Inc.     

Characterization of the denaturation of human alpha-lactalbumin in urea by molecular dynamics simulations

Molecular dynamics (MD) simulations were used to characterize the non-cooperative denaturation of the molten globule A-state of human alpha-lactalbumin by urea. A solvent of explicit urea and water molecules was used, corresponding to a urea concentration of approximately 6M. Three simulations were performed at temperatures of 293K, 360K and 400K, with lengths of 2 ns, 8 ns and 8 ns respectively. The results of the simulations were compared with experimental data from NMR studies of human alpha-lactalbumin and related peptides. During the simulations, hydrogen bonds were formed from the protein to both urea and water molecules as intra-protein hydrogen bonds were lost. Urea was shown to compete efficiently with water as both a hydrogen bond donor and acceptor. Radial distribution functions of water and urea around hydrophobic side chain atoms showed a significant increase in urea molecules in the solvation shell as the side chains became exposed during denaturation. A considerable portion of the native-like secondary structure persisted throughout the simulations. However, in the simulations at 360K and 400K, there were substantial changes in the packing of aromatic and other hydrophobic side chains in the protein, and many native contacts were lost. The results suggest that during the non-cooperative denaturation of the molten globule, secondary structure elements are stabilized by non-specific, non-native interactions.     

Force field influences in beta-hairpin folding simulations

All-atom force fields are now routinely used for more detailed understanding of protein folding mechanisms. However, it has been pointed out that use of all-atom force fields does not guarantee more accurate representations of proteins; in fact, sometimes it even leads to biased structural distributions. Indeed, several issues remain to be solved in force field developments, such as accurate treatment of implicit solvation for efficient conformational sampling and proper treatment of backbone interactions for secondary structure propensities. In this study, we first investigate the quality of several recently improved backbone interaction schemes in AMBER for folding simulations of a beta-hairpin peptide, and further study their influences on the peptide's folding mechanism. Due to the significant number of simulations needed for a thorough analysis of tested force fields, the implicit Poisson-Boltzmann solvent was used in all simulations. The chosen implicit solvent was found to be reasonable for studies of secondary structures based on a set of simulations of both alpha-helical and beta-hairpin peptides with the TIP3P explicit solvent as benchmark. Replica exchange molecular dynamics was also utilized for further efficient conformational sampling. Among the tested AMBER force fields, ff03 and a revised ff99 force field were found to produce structural and thermodynamic data in comparably good agreement with the experiment. However, detailed folding pathways, such as the order of backbone hydrogen bond zipping and the existence of intermediate states, are different between the two force fields, leading to force field-dependent folding mechanisms.     

Minimum model for the alpha-helix-beta-hairpin transition in proteins

We present a minimal model for proteins, which is able to capture the structural conversion between the alpha-helix and beta-hairpin. In most regimes of the parameter space, the model produces a stable structure at a low temperature; in a few limited regimes of the parameter space, the model displays an beta-hairpin transition as the physical conditions vary. These variations include a perturbation on hydrogen bonding propensity at the middle of the modeled chain, or the change of the hydrophobicity of a designated pair along the chain. Using Monte Carlo simulations, we demonstrate the structural conversion by means of state diagrams, heat capacity maps, and free energy maps.     

Analysis of the sequence and structural features of the left-handed beta-helical fold

The left-handed parallel beta-helix (LbetaH) is a structurally repetitive, highly regular, and symmetrical fold formed by coiling of elongated beta-sheets into helical "rungs." This canonical fold has recently received interest as a possible solution to the fibril structure of amyloid and as a building block of self-assembled nanotubular structures. In light of this interest, we aimed to understand the structural requirements of the LbetaH fold. We first sought to determine the sequence characteristics of the repeats by analyzing known structures to identify positional preferences of specific residues types. We then used molecular dynamics simulations to demonstrate the stabilizing effect of successive rungs and the hydrophobic core of the LbetaH. We show that a two-rung structure is the minimally stable LbetaH structure. In addition, we defined the structure-based sequence preference of the LbetaH and undertook a genome-wide sequence search to determine the prevalence of this unique protein fold. This profile-based LbetaH search algorithm predicted a large fraction of LbetaH proteins from microbial origins. However, the relative number of predicted LbetaH proteins per specie was approximately equal across the genomes from prokaryotes to eukaryotes.     

The ensemble folding kinetics of the FBP28 WW domain revealed by an all-atom Monte Carlo simulation in a knowledge-based potential

In this work, we apply a detailed all‐atom model with a transferable knowledge‐based potential to study the folding kinetics of Formin‐Binding protein, FBP28, which is a canonical three‐stranded β‐sheet WW domain. Replica exchange Monte Carlo simulations starting from random coils find native‐like (Cα RMSD of 2.68 Å) lowest energy structure. We also study the folding kinetics of FBP28 WW domain by performing a large number of ab initio Monte Carlo folding simulations. Using these trajectories, we examine the order of formation of two β‐hairpins, the folding mechanism of each individual β‐hairpin, and transition state ensemble (TSE) of FBP28 WW domain and compare our results with experimental data and previous computational studies. To obtain detailed structural information on the folding dynamics viewed as an ensemble process, we perform a clustering analysis procedure based on graph theory. Further, a rigorous P_fold analysis is used to obtain representative samples of the TSEs showing good quantitative agreement between experimental and simulated Φ values. Our analysis shows that the turn structure between first and second β strands is a partially stable structural motif that gets formed before entering the TSE in FBP28 WW domain and there exist two major pathways for the folding of FBP28 WW domain, which differ in the order and mechanism of hairpin formation. Proteins 2011. © 2011 Wiley‐Liss, Inc.     

Molecular dynamics simulations of the acyl-enzyme and the tetrahedral intermediate in the deacylation step of serine proteases

Despite the availability of many experimental data and some modeling studies, questions remain as to the precise mechanism of the serine proteases. Here we report molecular dynamics simulations on the acyl-enzyme complex and the tetrahedral intermediate during the deacylation step in elastase catalyzed hydrolysis of a simple peptide. The models are based on recent crystallographic data for an acyl-enzyme intermediate at pH 5 and a time-resolved study on the deacylation step. Simulations were carried out on the acyl enzyme complex with His-57 in protonated (as for the pH 5 crystallographic work) and deprotonated forms. In both cases, a water molecule that could provide the nucleophilic hydroxide ion to attack the ester carbonyl was located between the imidazole ring of His-57 and the carbonyl carbon, close to the hydrolytic position assigned in the crystal structure. In the "neutral pH" simulations of the acyl-enzyme complex, the hydrolytic water oxygen was hydrogen bonded to the imidazole ring and the side chain of Arg-61. Alternative stable locations for water in the active site were also observed. Movement of the His-57 side-chain from that observed in the crystal structure allowed more solvent waters to enter the active site, suggesting that an alternative hydrolytic process directly involving two water molecules may be possible. At the acyl-enzyme stage, the ester carbonyl was found to flip easily in and out of the oxyanion hole. In contrast, simulations on the tetrahedral intermediate showed no significant movement of His-57 and the ester carbonyl was constantly located in the oxyanion hole. A comparison between the simulated tetrahedral intermediate and a time-resolved crystallographic structure assigned as predominantly reflecting the tetrahedral intermediate suggests that the experimental structure may not precisely represent an optimal arrangement for catalysis in solution. Movement of loop residues 216-223 and P3 residue, seen both in the tetrahedral simulation and the experimental analysis, could be related to product release. Furthermore, an analysis of the geometric data obtained from the simulations and the pH 5 crystal structure of the acyl-enzyme suggests that since His-57 is protonated, in some aspects, this crystal structure resembles the tetrahedral intermediate.     

Prediction of the binding mode between GSK3β and a peptide derived from GSKIP using molecular dynamics simulation

GSK3β plays an important role in many physiological functions; dysregulated GSK3β is involved in human diseases such as diabetes, cancer, and Alzheimer's disease. This study uses MD simulations to determine the interaction between GSK3β and a peptide derived from GSKIP, a novel GSK3β interacting protein. Results show that GSKIPtide is inlaid in a binding pocket consisting of an α-helix and an extended loop near the carboxy-terminal end. This binding pocket is hydrophobic, and is responsible for the protein-protein interaction of two other GSK3β interacting proteins: FRAT and Axin. The GSKIPtide binding mode is closer to that of AxinGID (in the Axin-GSK3-interacting domain). The single-point mutations of V267G and Y288F in GSK3β differentiate the binding modes between GSK3 and GSKIPtide, AxinGID, and FRATide. The V2677G mutation of GSK3β reduces the GSKIPtide binding affinity by 70% and abolishes the binding affinity with AxinGID, but has no effect on FRATide. However, GSK3β Y288F completely abolishes the FRATide binding without affecting GSKIPtide or AxinGID binding. An analysis of the GSK3β-GSKIPtide complex structure and the X-ray crystal structures of GSK3β-FRATide and GSK3β-AxinGID complexes suggests that the hydroxyl group of Y288 is crucial to maintaining a hydrogen bond network in GSK3β-FRATide. The hydrophobic side chain of V267 maintains the integrity of helix-helix ridge-groove hydrophobic interaction for GSK3β-GSKIPtide and GSK3β-AxinGID. This study simulates these two mutant systems to provide atomic-level evidence of the aforementioned experimental results and validate the wild-type complex structure prediction.