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.     

Periodic force induced stabilization or destabilization of the denatured state of a protein

We have studied the effects of an external sinusoidal force in protein folding kinetics. The externally applied force field acts on the each amino acid residues of polypeptide chains. Our simulation results show that mean protein folding time first increases with driving frequency and then decreases passing through a maximum. With further increase of the driving frequency the mean folding time starts increasing as the noise-induced hoping event (from the denatured state to the native state) begins to experience many oscillations over the mean barrier crossing time period. Thus unlike one-dimensional barrier crossing problems, the external oscillating force field induces both stabilization or destabilization of the denatured state of a protein. We have also studied the parametric dependence of the folding dynamics on temperature, viscosity, non-Markovian character of bath in presence of the external field.     

Oscillatory molecular driving force for protein folding at high concentration: a molecular simulation

This paper presents a Langevin dynamics simulation that suggests a novel way to fold protein at high concentration, a fundamental issue in neurodegenerative diseases in vivo and the production of recombinant proteins in vitro. The simulation indicates that the folding of a coarse-grained beta-barrel protein at high concentration follows the "collapse-rearrangement" mechanism but it yields products of various forms, including single proteins in the native, misfolded, and uncollapsed forms and protein aggregates. Misfolded and uncollapased proteins are the "nucleus" of the aggregates that also encapsulate some correctly folded proteins (native proteins). An optimum hydrophobic interaction strength (epsilon*(p)) between the hydrophobic beads of the model protein, which results from a compromise between the kinetics of collapse and rearrangement, is identified for use in increasing the rate of folding over aggregating. Increased protein concentration hinders the structural transitions in both collapse and rearrangement and thus favors aggregation. A new method for protein folding at high concentration is proposed, which uses an oscillatory molecular driving force (epsilon*(p)) to promote the dissociation of aggregates in the low epsilon*(p) regime while promoting folding at a high epsilon*(p). The advantage of this method in enhancing protein folding while depressing aggregation is illustrated by a comparison with the methods based on direct dilution or applying a denaturant gradient.     

高分子链坍塌转变动力学过程的动态蒙特卡罗模拟

基于键长涨落格子模型和动态蒙特卡罗模拟方法,引入疏水相互作用,对均聚高分子链坍塌转变动力学过程进行了模拟研究.模拟发现,其坍塌时间呈高斯分布,而平均坍塌时间随淬火深度的变化类似于蛋白质折叠,但难以发现局部最小;另外,平均坍塌时间随链长呈指数形式变化.在其坍塌动力学过程中,高分子链构象先由橄榄球状演变为项链状,进而演变为香肠状,最后形成近球状的熔融球;基于团簇数目、团簇大小和非球面参数等参量,对前人提出的动力学过程四阶段划分进行了更为清晰的界定.     

Ab initio folding of helix bundle proteins using molecular dynamics simulations

We have demonstrated that ab initio fast folding simulations at 400 K using a GB implicit solvent model with an all-atom based force field can describe the spontaneous formation of nativelike structures for the 36-residue villin headpiece and the 46-residue fragment B of Staphylococcal protein A. An implicit solvent model combined with high-temperature MD makes it possible to perform direct folding simulations of small- to medium-sized proteins by reducing the computational requirements tremendously. In the early stage of folding of the villin headpiece and protein A, initial hydrophobic collapse and rapid formation of helices were found to play important roles. For protein A, the third helix forms first in the early stage of folding and exhibits higher stability. The free energy profiles calculated from the folding simulations suggested that both of the helix-bundle proteins show a two-state thermodynamic behavior and protein A exhibits rather broad native basins.     

The burial of solvent-accessible surface area is a predictor of polypeptide folding and misfolding as a function of chain elongation

The hydrophobic effect is a major driving force in all chemical and biological events involving chain collapse in aqueous solution. Here, we show that the burial of nonpolar solvent-accessible surface area (NSASA) is a powerful criterion to predict the folding and misfolding behavior of small single-domain proteins as a function of chain elongation. This bears fundamental implications for co- and post-translational protein folding in the cell and for understanding the interplay between noncovalent interactions and formation of native-like structure and topology. Comparison between the fraction of NSASA in fully unfolded and folded elongating chains shows that efficient burial of nonpolar surface area is preferentially achieved only when the polypeptide chain is almost complete. This effect has no preferential vectorial character in that it is present upon elongation from both the N and C termini. For incomplete chains that do not have the ability to fold and bury nonpolar surface intramolecularly, the overall hydrophobic nature of the polypeptide chain (expressed as FBA, i.e., fractional buried surface area per residue) dictates the tendency toward misfolding and self-association. N-terminal chains characterized by FBA exceeding 0.73 are likely to misfold and aggregate, if unable to fold intramolecularly.     

Folding versus self-assembling

Model foldable polymers with sequences of rigid hydrophobic chromophores and flexible hydrophilic tetra(ethylene glycol) were synthesized and used as a paradigm for studying molecular-folding and self-assembly phenomena. Our results demonstrate that intramolecular association or folding prevails over intermolecular interaction or self-assembling in the concentration region from 1 microM to 0.1 M. Importantly, folded polymeric nanostructures have absorption and fluorescence properties that are distinct from those of unfolded polymers or free monomers. We hypothesize that the origins of folding and self-assembly come from interactions between molecular units, and that the key parameter that regulates the on-and-off of such interactions is the distance R separating the two molecular units. Each molecular unit produces a characteristic force field, and when another molecular unit enters this field, the probability that the two units will interact increases significantly. A preliminary estimate of the radius of such a force field for the perylene tetracarboxylic diimide chromophore is about 90-120 A. As a result, phenomena associated with folding or self-assembly of molecular species are observed when these conditions are met in solution.     

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.     

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     

The interplay of turn formation and hydrophobic interactions on the early kinetic events in protein folding

While both turn formation and hydrophobic interactions play dominant roles in the initiation of protein folding, their individual contributions to the folding kinetics and to the structural stability of the protein still remain poorly understood. Here, we applied a photolabile linker to "cage" some important structural motifs, including both α-helices and β-sheets, into their non-native states. These "caged" structural motifs are then relaxed by laser-flash photolysis and their refolding events followed by photoacoustic calorimetry (PAC) and photothermal beam deflection (PBD). These experiments, combined with our previous results, revealed that spontaneous α-helix formation can occur extremely rapidly (10(8)-10(9) s(-1)) if the process is driven solely by turn formation followed by helix propagation. However, if sequestering of the side chains of hydrophobic amino acid residues participates in the refolding process, which may provide additional driving force beyond that afforded by turn formation alone, the refolding rate will be retarded, often by many orders of magnitude. This is usually the case in the formation of three-stranded β-sheets (10(7)-10(8) s(-1)) and β-hairpins (10(5)-10(6) s(-1)). Thus, we propose that proteins take advantage of the hierarchy of timescales associated with either turn formation, hydrophobic interactions, or global collapse of tertiary structure to accomplish the folding process in an orderly fashion, as these events are sufficiently separated in time and do not interfere with one another.     

The relative helix and hydrogen bond stability in the B domain of protein A as revealed by integrated tempering sampling molecular dynamics simulation

Molecular dynamics simulations using the integrated tempering sampling method were performed for the folding of wild-type B domain of protein A (BdpA). Starting from random and stretched structures, these simulations allow us to fold this protein into the native-like structure frequently, achieving very small backbone (1.7 A?) and all heavy-atom root-mean-square deviation (2.6 A?). Therefore, the method used here increases the efficiency of configuration sampling and thermodynamics characterization by molecular dynamics simulation. Although inconsistency exists between the calculation and experiments for the absolute stabilities, as a limitation of the force field parameters, the calculated order of helix stability (H3 > H2 > H1) is consistent with that determined by experiments for individual separate helices. The lowest free energy folding pathway of BdpA was found to start with a barrierless and non-cooperative structural collapse from the entirely extended (E) state, which leads to a physiologically unfolded (P) state consisting of multiple stable structures with few native inter-helical hydrophobic interactions formed. In the P state, only H3 is fully structured. The final formation of H1 (and to a lesser extent, H2) in the folded (F) state requires the packing of the inter-helical hydrophobic contacts. In addition, it was found that stabilities of backbone hydrogen bonds are significantly affected by their positions relative to the inter-helical hydrophobic core. As temperature increases, the stability of the hydrogen bonds exposed to the solvent tends to increase while that of the hydrogen bonds buried within the hydrophobic core decreases. Finally, we discuss implications of this study on the general folding mechanism of proteins.     

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.     

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.     

The driving force for co-translational protein folding is weaker in the ribosome vestibule due to greater water ordering

Interactions between the ribosome and nascent chain can destabilize folded domains in the ribosome exit tunnel''s vestibule, the last 3 nm of the exit tunnel where tertiary folding can occur. Here, we test if a contribution to this destabilization is a weakening of hydrophobic association, the driving force for protein folding. Using all-atom molecular dynamics simulations, we calculate the potential-of-mean force between two methane molecules along the center line of the ribosome exit tunnel and in bulk solution. Associated methanes, we find, are half as stable in the ribosome''s vestibule as compared to bulk solution, demonstrating that the hydrophobic effect is weakened by the presence of the ribosome. This decreased stability arises from a decrease in the amount of water entropy gained upon the association of the methanes. And this decreased entropy gain originates from water molecules being more ordered in the vestibule as compared to bulk solution. Therefore, the hydrophobic effect is weaker in the vestibule because waters released from the first solvation shell of methanes upon association do not gain as much entropy in the vestibule as they do upon release in bulk solution. These findings mean that nascent proteins pass through a ribosome vestibule environment that can destabilize folded structures, which has the potential to influence co-translational protein folding pathways, energetics, and kinetics.

In the ribosome vestibule, the contact minimum between two methane molecules is half as stable as compared to in bulk solution, demonstrating that the hydrophobic effect is weakened in the vestibule of ribosome exit tunnel.     

Critical importance of length-scale dependence in implicit modeling of hydrophobic interactions

The existence of length-scale dependence of hydrophobic solvation has important implications in the equilibrium of disordered, partially folded, and folded protein conformations. Neglecting this dependence, such as in popular solute surface-area based implicit solvent models with fixed surface tension coefficients, severely limits the ability to accurately model protein conformational equilibrium. We illustrate such fundamental limitations by examining the potentials of mean force of forming dimeric and trimeric nonpolar clusters and propose a new empirical model that effectively captures the context dependence of the local effective surface tension. Further optimization of the new model with other components of the implicit solvent force fields provides promise to significantly improve one's ability to simulate protein folding and conformational transitions. The existence of length-scale dependence of hydrophobic solvation has important implications in the equilibrium of disordered, partially folded, and folded protein conformations. Neglecting this dependence, such as in popular solute surface-area based implicit solvent models with fixed surface tension coefficients, severely limits the ability to accurately model protein conformational equilibrium. We illustrate such fundamental limitations by examining the potentials of mean force of forming dimeric and trimeric nonpolar clusters and propose a new empirical model that effectively captures the context dependence of the local effective surface tension. Further optimization of the new model with other components of the implicit solvent force fields provides promise to significantly improve one's ability to simulate protein folding and conformational transitions.     

A free-volume hole-filling model for the solubility of liquid molecules in glassy polymers 1: Model derivation

The use of hole-filling models is quite common for the sorption of gases into glassy polymers, but these have yet to be explicitly applied to the case of liquid immersion, where extensive use of Flory-Huggins theory dominates. This paper explores how the models based on the idea of sequential filling of a Gaussian distribution of pre-existing free-volume holes within the structure of the glassy polymer can be modified to allow the prediction of the equilibrium solubility of a liquid penetrant. For liquids, the driving force for sorption is more subtle than for gases, with more emphasis on molecular interactions rather than external pressure. For this reason, terms relating to the molecular interactions of a liquid molecule filling a hole were developed, including the effects of elastic constraint for small holes. Consideration of thermal fluctuations show that configurational entropy provides much of the driving force for sorption. Some comparisons with experimental data show a reasonable agreement, and one which is far better than the Flory-Huggins theory.     

Self-assembly of a dialkylurea gelator in organic solvents in the presence of centrifugal and shearing forces

A novel dialkylurea gelator, 1-methyl-2,4-bis(N(')-octadecaneureido)benzene (designated as MBOB) was synthesized, which can turn some organic solvents into organogels at extremely low concentrations (<2 wt%). The (1)H NMR spectra of MBOB in solution (110 degrees C) and in the gel state (30 degrees C) indicate that intermolecular hydrogen bonding is the driving force for the self-assembly of MBOB. In the process of the self-assembly of MBOB, orientation of MBOB aggregates occurs under the influence of external fields, such as a centrifugal force and shearing force fields. The minimum gelation concentrations of MBOB in organic solvents under a centrifugal force field were significantly higher than those in the absence of a centrifugal force field, indicating a significant effect of the external field on the self-assembly of MBOB. Field emission scanning electron microscopy (FE-SEM) provided evidence for a significantly phase transition of the MBOB aggregates from an amorphous state in the absence of the external field to an oriented state under conditions of a centrifugal or shearing force during the gelation process. A self-assembled structure of MBOB is proposed based upon an X-ray diffraction (XRD) analysis and a molecular simulation. DSC analysis of the organogels indicates that the phase transition temperature increased from 58.5 degrees C in the absence of the external field to 63.3 degrees C under a centrifugal force field and 62.2 degrees C under a shearing force field. The enthalpy of the phase transition decreased from 3.1 J/g in the absence of an external field to 2.6 J/g under a centrifugal force field and 2.7 J/g under a shearing force field.     

Efficient molecular mechanics simulations of the folding,orientation, and assembly of peptides in lipid bilayers using an implicit atomic solvation model

Membrane proteins comprise a significant fraction of the proteomes of sequenced organisms and are the targets of approximately half of marketed drugs. However, in spite of their prevalence and biomedical importance, relatively few experimental structures are available due to technical challenges. Computational simulations can potentially address this deficit by providing structural models of membrane proteins. Solvation within the spatially heterogeneous membrane/solvent environment provides a major component of the energetics driving protein folding and association within the membrane. We have developed an implicit solvation model for membranes that is both computationally efficient and accurate enough to enable molecular mechanics predictions for the folding and association of peptides within the membrane. We derived the new atomic solvation model parameters using an unbiased fitting procedure to experimental data and have applied it to diverse problems in order to test its accuracy and to gain insight into membrane protein folding. First, we predicted the positions and orientations of peptides and complexes within the lipid bilayer and compared the simulation results with solid-state NMR structures. Additionally, we performed folding simulations for a series of host–guest peptides with varying propensities to form alpha helices in a hydrophobic environment and compared the structures with experimental measurements. We were also able to successfully predict the structures of amphipathic peptides as well as the structures for dimeric complexes of short hexapeptides that have experimentally characterized propensities to form beta sheets within the membrane. Finally, we compared calculated relative transfer energies with data from experiments measuring the effects of mutations on the free energies of translocon-mediated insertion of proteins into lipid bilayers and of combined folding and membrane insertion of a beta barrel protein.     

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.