Enhanced Wang Landau sampling of adsorbed protein conformations

Using computer simulations to model the folding of proteins into their native states is computationally expensive due to the extraordinarily low degeneracy of the ground state. In this paper, we develop an efficient way to sample these folded conformations using Wang Landau sampling coupled with the configurational bias method (which uses an unphysical "temperature" that lies between the collapse and folding transition temperatures of the protein). This method speeds up the folding process by roughly an order of magnitude over existing algorithms for the sequences studied. We apply this method to study the adsorption of intrinsically disordered hydrophobic polar protein fragments on a hydrophobic surface. We find that these fragments, which are unstructured in the bulk, acquire secondary structure upon adsorption onto a strong hydrophobic surface. Apparently, the presence of a hydrophobic surface allows these random coil fragments to fold by providing hydrophobic contacts that were lost in protein fragmentation.     

A minimal proteinlike lattice model: an alpha-helix motif

A simple protein model of a four-helix bundle motif on a face-centered cubic lattice has been studied. Total energy of a conformation includes attractive interactions between hydrophobic residues, repulsive interactions between hydrophobic and polar residues, and a potential that favors helical turns. Using replica exchange Monte Carlo simulations we have estimated a set of parameters for which the native structure is a global minimum of conformational energy. Then we have shown that all the above types of interactions are necessary to guarantee the cooperativity of folding transition and to satisfy the thermodynamic hypothesis.     

Hydrophobic collapse in (in silico) protein folding

A model of hydrophobic collapse, which is treated as the driving force for protein folding, is presented. This model is the superposition of three models commonly used in protein structure prediction: (1) 'oil-drop' model introduced by Kauzmann, (2) a lattice model introduced to decrease the number of degrees of freedom for structural changes and (3) a model of the formation of hydrophobic core as a key feature in driving the folding of proteins. These three models together helped to develop the idea of a fuzzy-oil-drop as a model for an external force field of hydrophobic character mimicking the hydrophobicity-differentiated environment for hydrophobic collapse. All amino acids in the polypeptide interact pair-wise during the folding process (energy minimization procedure) and interact with the external hydrophobic force field defined by a three-dimensional Gaussian function. The value of the Gaussian function usually interpreted as a probability distribution is treated as a normalized hydrophobicity distribution, with its maximum in the center of the ellipsoid and decreasing proportionally with the distance versus the center. The fuzzy-oil-drop is elastic and changes its shape and size during the simulated folding procedure.     

Folding Dynamics of 10‐Residue β‐Hairpin Peptide Chignolin

Short peptides that fold into β‐hairpins are ideal model systems for investigating the mechanism of protein folding because their folding process shows dynamics typical of proteins. We performed folding, unfolding, and refolding molecular dynamics simulations (total of 2.7 μs) of the 10‐residue β‐hairpin peptide chignolin, which is the smallest β‐hairpin structure known to be stable in solution. Our results revealed the folding mechanism of chignolin, which comprises three steps. First, the folding begins with hydrophobic assembly. It brings the main chain together; subsequently, a nascent turn structure is formed. The second step is the conversion of the nascent turn into a tight turn structure along with interconversion of the hydrophobic packing and interstrand hydrogen bonds. Finally, the formation of the hydrogen‐bond network and the complete hydrophobic core as well as the arrangement of side‐chain–side‐chain interactions occur at approximately the same time. This three‐step mechanism appropriately interprets the folding process as involving a combination of previous inconsistent explanations of the folding mechanism of the β‐hairpin, that the first event of the folding is formation of hydrogen bonds and the second is that of the hydrophobic core, or vice versa.     

A ternary nucleation model for the nucleation pathway of protein folding

Recently [Y. S. Djikaev and E. Ruckenstein, J. Phys. Chem. B 111, 886 (2007)], the authors proposed a kinetic model for the nucleation mechanism of protein folding where a protein was modeled as a heteropolymer consisting of hydrophobic and hydrophilic beads and the composition of the growing cluster of protein residues was assumed to be constant and equal to the overall protein composition. Here, they further develop the model by considering a protein as a three-component heteropolymer and by allowing the composition of the growing cluster of protein residues to vary independently of the overall one. All the bonds in the heteropolymer (now consisting of hydrophobic, hydrophilic, and neutral beads) have the same constant length, and all the bond angles are equal and fixed. As a crucial idea of the model, an overall potential around the cluster wherein a residue performs a chaotic motion is considered to be a combination of the average dihedral and average pairwise potentials assigned to the bead. The overall potential as a function of the distance from the cluster center has a double well shape which allows one to determine its emission and absorption rates by using a first passage time analysis. Knowing these rates as functions of three independent variables of a ternary cluster, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein using a ternary nucleation formalism and evaluate the size and composition of the nucleus and the protein folding time. As an illustration, the model is applied to the folding of bovine pancreatic ribonuclease consisting of 124 amino acids whereof 40 are hydrophobic, 81 hydrophilic, and 3 neutral. With a reasonable choice of diffusion coefficients of the residues in the native state and potential parameters, the model predicts folding times in the range of 1-100 s.     

Self-organization in protein folding and the hydrophobic interaction

Self-organization is a critical aspect of living systems. During the folding of protein molecules, the hydrophobic interaction plays an important role in the collapse of the peptide chain to a compact shape. As the hydrophobic core tightens and excludes water, not only does the number of hydrophobic side chain contacts increase, but stabilization is further enhanced by an increase in strength of each hydrophobic interaction between side chains in the core. Thus, the self-organization of the protein folding process augments itself by enhancing the stability of the core against large-scale motions that would unfold the protein. Through calculations and computer simulations on a model four-helix bundle protein, we show how the strengthening of the hydrophobic interaction is crucial for stabilizing the core long enough for completion of the folding process and quantitatively manifests self-organizing dynamical behavior.     

Dynamic redox environment-intensified disulfide bond shuffling for protein refolding in vitro: molecular simulation and experimental validation

One challenge in protein refolding is to dissociate the non-native disulfide bonds and promote the formation of native ones. In this study, we present a coarse-grained off-lattice model protein containing disulfide bonds and simulate disulfide bond shuffling during the folding of this model protein. Introduction of disulfide bonds in the model protein led to enhanced conformational stability but reduced foldability in comparison to counterpart protein without disulfide bonds. The folding trajectory suggested that the model protein retained the two-step folding mechanism in terms of hydrophobic collapse and structural rearrangement. The disulfide bonds located in the hydrophobic core were formed before the collapsing step, while the bonds located on the protein surface were formed during the rearrangement step. While a reductive environment at the initial stage of folding favored the formation of native disulfide bonds in the hydrophobic core, an oxidative environment at a later stage of folding was required for the formation of disulfide bonds at protein surface. Appling a dynamic redox environment, that is, one that changes from reductive to oxidative, intensified disulfide bond shuffling and thus resulted in improved recovery of the native conformation. The above-mentioned simulation was experimentally validated by refolding hen-egg lysozyme at different urea concentrations and oxidized glutathione/reduced glutathione (GSSG/GSH) ratios, and an optimal redox environment, in terms of the GSSG to GSH ratio, was identified. The implementation of a dynamic redox environment by tuning the GSSG/GSH ratio further improved the refolding yield of lysozyme, as predicted by molecular simulation.     

Folding mechanisms of individual beta-hairpins in a Go model of Pin1 WW domain by all-atom molecular dynamics simulations

This paper examines the folding mechanism of an individual beta-hairpin in the presence of other hairpins by using an off-lattice model of a small triple-stranded antiparallel beta-sheet protein, Pin1 WW domain. The turn zipper model and the hydrophobic collapse model originally developed for a single beta-hairpin in literature is confirmed to be useful in describing beta-hairpins in model Pin1 WW domain. We find that the mechanism for folding a specific hairpin is independent of whether it folds first or second, but the formation process are significantly dependent on temperature. More specifically, beta1-beta2 hairpin folds via the turn zipper model at a low temperature and the hydrophobic collapse model at a high temperature, while the folding of beta2-beta3 hairpin follows the turn zipper model at both temperatures. The change in folding mechanisms is interpreted by the interplay between contact stability (enthalpy) and loop lengths (entropy), the effect of which is temperature dependent.     

Denatured-state ensemble and the early-stage folding of the G29A mutant of the B-domain of protein A

The folding mechanism of the G29A mutant of the B-domain of protein A (BdpA) has been studied by all-atom molecular dynamics simulation using AMBER force field (ff03) and generalized Born continuum solvent model. Started from the extended chain conformation, a total of 16 simulations (400 ns each) at 300 K captured some early folding events of the G29A mutant of BdpA. In one of the 16 trajectories, the G29A mutant folded within 2.8 A (root mean square) of the wild-type NMR structure. We observed that the fast burial of hydrophobic residues was the driving force to bring the distant residues into close proximity. The initiation of the helix I and III occurred during the stage of hydrophobic collapse. The initiation and growth of the helix II was slow. Both the secondary structure formation and the development of the native tertiary contacts suggested a multistage folding process. Clustering analysis indicated that two helix species (helices I and III) could be intermediates. Further analysis revealed that the hydrophobic residues of partially folded helix II formed nativelike hydrophobic contacts with helices I and III that stabilized a nativelike state and delayed the completion of folding of the entire protein. The details of the early folding process were compared with other theoretical and experimental studies. It was found that a nativelike hydrophobic cluster was formed by residues including F(30), I(31), L(34), L(44), L(45), and A(48) that prevented further development of the native structures, and breaking the hydrophobic cluster like this one contributed to the rate-limiting step. This was in complete agreement with the recent kinetic measurements in which mutations of these residues to Gly and Ala substantially increased the folding rates by as much as 60 times. Apparently, destabilization of nonnative states dramatically enhanced the folding rates.     

Polar confinement modulates solvation behavior of methane molecules

Polar confinement induces an amorphous solidlike state of water characterized by an orientational correlation time longer than hundreds of picoseconds and significant structural disorder. Solvation behavior of methane molecules is dramatically modulated under polar confinement. Moreover our simulations indicate that the charges equivalent to those borne by atoms of amino acids could generate an electric field which is strong enough to stimulate the phase transition of water. In our results, polar confinement is found to be more capable of aggregating hydrophobic molecules. This study raises an interesting mechanism by which the cagelike structure of the Escherichia coli chaperonin GroEL and the cochaperonin GroES complex helps protein folding.     

Thermodynamics and kinetics of a Gō proteinlike heteropolymer model with two-state folding characteristics

We present results of Monte Carlo computer simulations of a coarse-grained hydrophobic-polar Gō-like heteropolymer model and discuss thermodynamic properties and kinetics of an exemplified heteropolymer, exhibiting two-state folding behavior. It turns out that general, characteristic folding features of realistic proteins with a single free-energy barrier can also be observed in this simplified model, where the folding transition is primarily driven by the hydrophobic force.     

Analysis and prediction of protein folding rates using quadratic response surface models

Understanding the relationship between amino acid sequences and folding rates of proteins is an important task in computational and molecular biology. In this work, we have systematically analyzed the composition of amino acid residues for proteins with different ranges of folding rates. We observed that the polar residues, Asn, Gln, Ser, and Lys, are dominant in fast folding proteins whereas the hydrophobic residues, Ala, Cys, Gly, and Leu, prefer to be in slow folding proteins. Further, we have developed a method based on quadratic response surface models for predicting the folding rates of 77 two- and three-state proteins. Our method showed a correlation of 0.90 between experimental and predicted protein folding rates using leave-one-out cross-validation method. The classification of proteins based on structural class improved the correlation to 0.98 and it is 0.99, 0.98, and 0.96, respectively, for all-alpha, all-beta, and mixed class proteins. In addition, we have utilized Baysean classification theory for discriminating two- and three-state proteins, which showed an accuracy of 90%. We have developed a web server for predicting protein folding rates and it is available at http://bioinformatics.myweb.hinet.net/foldrate.htm.     

Dynamic folding pathway models of the villin headpiece subdomain (HP‐36) structure

We have investigated the folding pathway of the 36‐residue villin headpiece subdomain (HP‐36) by action‐derived molecular dynamics simulations. The folding is initiated by hydrophobic collapse, after which the concurrent formation of full tertiary structure and α‐helical secondary structure is observed. The collapse is observed to be associated with a couple of specific native contacts contrary to the conventional nonspecific hydrophobic collapse model. Stable secondary structure formation after the collapse suggests that the folding of HP‐36 follows neither the framework model nor the diffusion‐collision model. The C‐terminal helix forms first, followed by the N‐terminal helix positioned in its native orientation. The short middle helix is shown to form last. Signs for multiple folding pathways are also observed. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Reversed-phase liquid chromatography as a tool in the determination of the hydrophilicity/hydrophobicity of amino acid side-chains at a ligand-receptor interface in the presence of different aqueous environments. I. Effect of varying receptor hydrophobicity

We have developed further a chromatographic model for studying the hydrophobic interactions which characterize the way a ligand binds to its receptor. This model is based on observing the retention behaviour of de novo designed model 18-residue amphipathic alpha-helical peptides (representing the hydrophobic binding domain of a ligand) on reversed-phase packings by varying hydrophobicity (representing a receptor protein with a hydrophobic binding pocket). Mutants of the "native" peptide ligand (which contains seven Leu residues in its non-polar face) were designed by replacing one residue in the center of the extremely non-polar face of the amphipathic alpha-helix. Through reversed-phase liquid chromatography of these peptides at pH 2.0 on cyano and C18 columns, we have demonstrated how an increase in receptor hydrophobicity (represented by an increase in column stationary phase hydrophobicity; cyano --> C18) significantly enhances hydrophilicity of polar amino acid side-chains at the ligand-receptor interface while moderately enhancing the hydrophobicity of non-polar side-chains. The addition of salt (100 mM sodium perchlorate) to the aqueous environment surrounding the binding site of receptor and ligand was also shown to have a profound effect on side-chain hydrophilicity/hydrophobicity in the binding interface. This effect was particularly dramatic for the positively charged side-chains Arg, Lys and His, whose significant enhancement of hydrophobicity in the presence of the cyano column contrasted with their increase in hydrophilicity in the presence of the considerably more hydrophobic C18 stationary phase. Our results have major implications to understanding the influence of hydrophobic and aqueous environment on hydrophilicity/hydrophobicity of amino acid side-chains and the role side-chains play in the folding and stability of proteins.     

Folding and translocation of the undecamer of poly-L-leucine across the water-hexane interface. A molecular dynamics study.

The undecamer of poly-L-leucine at the water-hexane interface is studied by molecular dynamics simulations. This represents a simple model relevant to folding and insertion of hydrophobic peptides into membranes. The peptide, initially placed in a random coil conformation on the aqueous side of the system, rapidly translocates toward the hexane phase and undergoes interfacial folding into an alpha-helix in the subsequent 36 ns. Folding is nonsequential and highly dynamic. The initially formed helical segment at the N-terminus of the undecamer becomes transiently broken and, subsequently, reforms before the remainder of the peptide folds from the C-terminus. The formation of intramolecular hydrogen bonds during the folding of the peptide is preceded by a dehydration of the participating polar groups, as they become immersed in hexane. Folding proceeds through a short-lived intermediate, a 3(10)-helix, which rapidly interconverts to an alpha-helix. Both helices contribute to the equilibrium ensemble of folded structures. The helical peptide is largely buried in hexane, yet remains adsorbed at the interface. Its preferred orientation is parallel to the interface, although the perpendicular arrangement with the N-terminus immersed in hexane is only slightly less favorable. In contrast, the reversed orientation is highly unfavorable, because it would require dehydration of C-terminus carbonyl groups that do not participate in intramolecular hydrogen bonding. For the same reason, the transfer of the undecamer from the interface to the bulk hexane is also unfavorable. The results suggest that hydrophobic peptides fold in the interfacial region and, simultaneously, translocate into the nonpolar side of the interface. It is further implied that peptide insertion into the membrane is accomplished by rotating from the parallel to the perpendicular orientation, most likely in such a way that the N-terminus penetrates the bilayer.     

Embedded conformon model of chain folding

The real-space renormalization-group technique is used to study the low lying energy states of a random copolymer composed of hydrophobic (H) and polar (P) beads on a simple cubic lattice. Application of a variety of boundary conditions to parts of the larger chain (embedded conformons) while progressively increasing the length scale gives the lowest energy states in agreement with exact calculations for a 17 bead chain with a random H,P sequence. These results are significant for studying minimalist models of the folding of complex molecules because the computation time is several orders of magnitude less than for other approaches.     

Turn-directed folding dynamics of β-hairpin-forming de novo decapeptide Chignolin

Realistic mechanistic pictures of β-hairpin formation, offering valuable insights into some of the key early events in protein folding, are accessible through short designed polypeptides as they allow atomic-level scrutiny through simulations. Here, we present a detailed picture of the dynamics and mechanism of β-hairpin formation of Chignolin, a de novo decapeptide, using extensive, unbiased molecular dynamics simulations. The results provide clear evidence for turn-directed broken-zipper folding and reveal details of turn nucleation and cooperative progression of turn growth, hydrogen-bond formations, and eventual packing of the hydrophobic core. Further, we show that, rather than driving folding through hydrophobic collapse, cross-strand side-chain packing could in fact be rate-limiting as packing frustrations can delay formation of the native hydrophobic core prior to or during folding and even cause relatively long-living misfolded or partially folded states that may nucleate aggregative events in more complex situations. The results support the increasing evidence for turn-centric folding mechanisms for β-hairpin formation suggested recently for GB1 and Peptide 1 based on experiments and simulations but also point to the need for similar examinations of polypeptides with larger numbers of cross-strand hydrophobic residues.     

The effect of sequence on the conformational stability of a model heteropolymer in explicit water

We investigate the properties of a two-dimensional lattice heteropolymer model for a protein in which water is explicitly represented. The model protein distinguishes between hydrophobic and polar monomers through the effect of the hydrophobic monomers on the entropy and enthalpy of the hydrogen bonding of solvation shell water molecules. As experimentally observed, model heteropolymer sequences fold into stable native states characterized by a hydrophobic core to avoid unfavorable interactions with the solvent. These native states undergo cold, pressure, and thermal denaturation into distinct configurations for each type of unfolding transition. However, the heteropolymer sequence is an important element, since not all sequences will fold into stable native states at positive pressures. Simulation of a large collection of sequences indicates that these fall into two general groups, those exhibiting highly stable native structures and those that do not. Statistical analysis of important patterns in sequences shows a strong tendency for observing long blocks of hydrophobic or polar monomers in the most stable sequences. Statistical analysis also shows that alternation of hydrophobic and polar monomers appears infrequently among the most stable sequences. These observations are not absolute design rules and, in practice, these are not sufficient to rationally design very stable heteropolymers. We also study the effect of mutations on improving the stability of the model proteins, and demonstrate that it is possible to obtain a very stable heteropolymer from directed evolution of an initially unstable heteropolymer.     

Effect of ionized protein residues on the nucleation pathway of protein folding

Using a ternary nucleation formalism, we have recently [Y. S. Djikaev and E. Ruckenstein, J. Chem. Phys. 126, 175103 (2007)] proposed a kinetic model for the nucleation mechanism of protein folding. A protein was considered as a heteropolymer consisting of hydrophobic, hydrophilic, and neutral beads with all the bonds having the same constant length and all the bond angles equal and fixed. In this paper, we further develop that model by taking into account of the ionizability of some of the protein residues. As previously, an overall potential around the cluster wherein a protein residue performs a chaotic motion is considered to be a combination of the average dihedral and average pairwise potentials (the latter now including an electrostatic contribution for ionized residues) assigned to the residue and the confining potential due to the polymer connectivity constraint. The overall potential as a function of the distance from the cluster has a double well shape (even for ionized beads) which allows one to determine the rates of emission and absorption of residues by the cluster by using a first passage time analysis. Assuming the equality of the ratios of the numbers of negatively and positively ionized residues in the cluster and in the entire protein, one can keep the modified model within the framework of the ternary nucleation formalism and evaluate the size and composition of the nucleus and the protein folding time as in the previous model. As an illustration, the model is again applied to the folding of bovine pancreatic ribonuclease consisting of 124 amino acids, whereof 40 are hydrophobic, 81 hydrophilic (of which 10 are negatively and 18 positively ionizable), and 3 neutral. Numerical calculations at pH=6.3, pH=7.3, and pH=8.3 show that for this protein the time of folding via nucleation is significantly affected by electrostatic interactions only for the unusually low pH of 6.3 and that among all pH's considered pH=7.3 provides the lowest folding time.     

Probing the hydrophobic effect of noncovalent complexes by mass spectrometry

The study of noncovalent interactions by mass spectrometry has become an active field of research in recent years. The role of the different noncovalent intermolecular forces is not yet fully understood since they tend to be modulated upon transfer into the gas phase. The hydrophobic effect, which plays a major role in protein folding, adhesion of lipid bilayers, etc., is absent in the gas phase. Here, noncovalent complexes with different types of interaction forces were investigated by mass spectrometry and compared with the complex present in solution. Creatine kinase (CK), glutathione S-transferase (GST), ribonuclease S (RNase S), and leucine zipper (LZ), which have dissociation constants in the nM range, were studied by native nanoelectrospray mass spectrometry (nanoESI-MS) and matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) combined with chemical cross-linking (XL). Complexes interacting with hydrogen bonds survived the transfer into gas phase intact and were observed by nanoESI-MS. Complexes that are bound largely by the hydrophobic effect in solution were not detected or only at very low intensity. Complexes with mixed polar and hydrophobic interactions were detected by nanoESI-MS, most likely due to the contribution from polar interactions. All noncovalent complexes could easily be studied by XL MALDI-MS, which demonstrates that the noncovalently bound complexes are conserved, and a real “snap-shot” of the situation in solution can be obtained.