Smoothing of the GB1 Hairpin Folding Landscape by Interfacial Confinement

Abstract

We study the effects of confinement between planar walls on the folding thermodynamics of a β-hairpin, using large-scale replica-exchange molecular-dynamics simulations with an all-atom model and explicit solvent. We find that the folding free-energy landscape of this peptide observed in bulk is significantly modified when the peptide is confined between the walls. Most notably, the propensity of the peptide to form a misfolded state observed in the bulk solution becomes negligible under confinement. The absence of the misfolded state under confinement can be explained by an increased tendency of hydrophobic aromatic side chains to stay near the walls, because the misfolded state is characterized by a nonnative arrangement of aromatic side chains. These results from a simple confinement model may provide clues about the role of chaperonin confinement in smoothing folding landscapes by avoiding trapped intermediates.

Introduction

Protein folding in vivo is expected to differ from bulk solution owing to the extremely crowded conditions encountered in the cell (1) and the presence of cellular machinery, such as chaperones, that can assist folding by preventing misfolding and aggregation (2). Several plausible mechanisms of chaperonin function have been proposed, and it has been suggested that extreme protein confinement inside a chaperone cavity may be an important factor. Brinker et al. (3) hypothesized that confinement of an unfolded protein inside a GroEL/GroES chaperonin system may smoothen the energy landscape by preventing the population of kinetically trapped intermediates. Folding of proteins may also be coupled directly to their synthesis, commonly referred to as cotranslational folding, during which newly synthesized proteins emerge out of the narrow ribosome tunnel (4,5). The potential importance of confinement on protein folding is thus well recognized in the literature.

Confinement of a polymer-like protein chain to an inert space has been theoretically shown to stabilize the compact folded state entropically with respect to the expanded unfolded state (6–8). A more recent simulation study by Ziv et al. (9) showed that confinement in a cylindrical cavity mimicking a ribosome exit tunnel can also entropically stabilize α helices. Protein stabilization for a β-protein in a spherical pore was reported by Klimov and Thirumalai (10). Friedel et al. (11) and Baumketner et al. (12) found that long-lived intermediates present in bulk have shorter lifetimes when the protein is confined. Similar protein stabilization was also observed for proteins confined in silica pores in laboratory experiments (13,14). Mukherjee et al. (15) showed that one can tune the helicity of alanine-rich peptides confined within AOT reverse micelles by varying the degree of hydration.

It is worth mentioning that most previous simulation studies employed coarse-grained protein models in which solvent effects were included in a very indirect manner. Investigators have made significant advances in the development of implicit-solvent methods (16,17), and for protein folding in bulk, such models have been reasonably successful. However, current models do not describe the hydrophobic effect, which is critical for protein folding, very well. In addition, they may not be able to capture all of the effects of confinement on folding. This is partly because water behavior and hydrophobic effects under confinement are not well understood (18). Hence, it becomes imperative to consider the solvent explicitly in a simulation model to obtain an accurate description of confinement effects. Lucent et al. (19) performed the first such study using a distributed computing environment (Folding@home) on an α-helical protein, the villin headpiece domain. They found that protein confinement alone stabilized the folded state. However, when both the protein and solvent were confined in a repulsive spherical cavity, the folded state was actually destabilized. This observed destabilization is in contrast to most previous work on protein confinement in a repulsive pore, and clearly highlights the essential role of solvent in protein folding under confinement.

The repulsive interactions between a protein and confining walls are a simplification to represent physical boundaries in a system without any direct affinity of the protein for the wall. It is known that attractive interactions between confinement boundaries and protein molecules can affect protein behavior significantly. A comprehensive study using a coarse-grained protein model showed that a protein populates new conformations under attractive confinement (20). The modified protein conformations near an attractive surface can be useful in surface-assisted peptide folding to achieve a specific functional state (21). In a related study on attractive crowding (22), it was shown that attractive interactions can counteract the entropic stabilizing influence of repulsive crowders. Mukherjee et al. (23) also found that the folding rate of a β-hairpin peptide can decrease in the presence of common crowding agents, a result that cannot be explained solely on the basis of excluded volume effects of crowding agents. However, we are not aware of any previous work in which investigators studied the influence of attractive confining boundaries using an all-atom protein-folding model, including explicit solvent. Any biological surface (chaperonin surface or large protein assembly) that is modeled with simple confining boundaries must include attractive interactions in some form.

In this work, we investigate the folding of a β-hairpin under the influence of an attractive planar confinement (Fig. 1) using an all-atom representation of the peptide and the solvent. The planar confinement between rectangular walls can serve as a basic model for studies of more complicated confined systems in the future. We previously performed extensive studies on the folding thermodynamics and kinetics of the β-hairpin in bulk; hence, its bulk behavior is well understood (24–26). Although this system may be significantly smaller than typical chaperonin substrates, its size permits a thorough equilibrium sampling, and it includes representative features of the folding of larger proteins, i.e., it folds in an approximately two-state fashion but also includes stable nonnative states. Specifically, in our previous studies we found that this peptide populates a misfolded state in which one strand of the hairpin is flipped and the hydrophobic side chains on the two strands are found on opposite faces of the hairpin. Here, we find that when this peptide is confined between two planar attractive walls, this misfolded state completely disappears from the free-energy surface. We find that the misfolded state is destabilized because hydrophobic side chains are most likely to be found on the same side due to their interactions with confining walls. Although these results were obtained from a very simple confinement model, they may provide insights into the role of chaperonin confinement in tackling protein misfolding by nonspecific weak interactions.

Figure 1.

Model system. Schematics of the GB1 hairpin solvated in bulk water (A) and confined between planar Lennard Jones walls with two different separation distances (B and C) are shown.

Materials and Methods

Simulation details

We used the Amber ff03^∗ force field (24,27) for the peptide because it has been shown to alleviate biases toward a particular secondary structure (28), and the TIP3P model (29) for water, consistent with our earlier studies on this peptide in bulk. The structure of the 16-residue GB1 hairpin was taken from residues 41–56 of the full-length GB1 protein (Protein Data Bank ID: 1GB1). The protein was solvated using 3234 water molecules, and eight sodium and five chloride ions were added to neutralize the charge. To simulate confined systems with explicit solvent, we chose the separation between the walls to be 1.8 nm and 2.4 nm, respectively. Simulation boxes of dimensions 5.0233×5.0233×1.8 nm³ and 4.1645×4.1645×2.4 nm³ were used for the two cases, respectively, and periodic boundary conditions were applied in the x and y directions only. To enhance equilibrium sampling, we performed replica-exchange molecular-dynamics (REMD) (30) simulations in the NVT ensemble using 32 replicas spanning a temperature range of 278–595 K for 500 ns per replica. We used the following temperatures (in K): 278, 287, 295, 303, 312, 321, 329, 338, 346, 355, 365, 375, 385, 396, 406, 416, 427, 437, 448, 459, 470, 482, 493, 505, 517, 528, 539, 551, 562, 573, 584, and 595. The particle mesh Ewald method (31) was used to calculate electrostatic interactions with a real-space cutoff of 0.9 Å. The cutoff for van der Waals interactions was taken to be 1.4 Å, and the parameters of the Lennard-Jones potential for the cross interactions between the nonbonded atoms were obtained from the Lorentz-Berthelot combination rules. The attractive confining walls were modeled using the Lennard-Jones 9-3 potential V given by

$$V\left(z\right)=\mathit{ϵ}\left[\frac{2}{15}{\left(\frac{\sigma }{z}\right)}^9-{\left(\frac{\sigma }{z}\right)}^3\right],$$ (1)

where z is the distance of an atom (peptide and solvent) from the wall, σ is the characteristic length scale, and ε is the characteristic energy scale. To simulate stable liquid water between planar walls (32), the values of ${\sigma }_{\text{wall}-\text{OW}}$ = 0.346 nm and ${\mathit{ϵ}}_{\text{wall}-\text{OW}}$ = 1.14 kcal/mol were used. All simulations were performed using GROMACS 4.0.4 (33).

Reaction coordinates

The fraction of ordered contacts, $Q_s$, relative to a given structure, s (not necessarily the native state), is defined as

$$Q_s=N_s^{-1}\sum _{\left(i,j\right)}\frac{1}{1+\text{exp}\left(\gamma \left(r_{ij}-\lambda r_{ij}^0\right)\right)}$$ (2)

where the sum runs over the $N_s$ pairs $\left(i,j\right)$ of native atomic contacts that are separated by distances $r_{ij}$ in the configuration of interest and by $r_{ij}^0$ in s (γ = 5 Å⁻¹; λ = 1.5). The parameter λ accounts for the fluctuations in distance between the residues in contact in the native state, and γ controls the steepness of the contact step function (24).

One of the reaction coordinates chosen, the fraction of all-atom (excluding hydrogen atoms) native contacts, $Q_{aa}$, is defined using the native structure (Fig. 2 C, inset). $Q_{aa}$ has been shown to be a very good reaction coordinate (34). $Q_{aa}$ has a low value when the protein is unfolded and a value near unity for a folded state. However, this coordinate is not suitable for distinguishing between folded and misfolded states. In the misfolded structure of the hairpin, one of the strands of the hairpin is flipped (26) (Fig. 2 A, inset, and Fig. S1 A in the Supporting Material). To separate this native-like off-pathway intermediate, which would otherwise stay close to the folding transition state on $Q_{aa}$, an alternative coordinate, $Q_{n-nn}$, is chosen (26). $Q_{n-nn}$, based on Eq. 2, is defined as $Q_{n-nn}=Q_n-Q_{nn}$, where $Q_n$ and $Q_{nn}$ are defined as above using the native and misfolded (Fig. S1 A) structures, respectively. For both $Q_{aa}$ and $Q_{n-nn}$, atom pairs closer than 4.5 Å in s, belonging to residues separated by >3 in the sequence, are considered.

Figure 2.

Free-energy landscapes. Two-dimensional free-energy surfaces at 303 K are shown as a function of the order parameters $Q_{n-nn}$ and $Q_{aa}$ (see text) for GB1 hairpin in bulk water (A) and confined between walls with separation distance of 1.8 nm (B) and 2.4 nm (C). The misfolded state, characterized by flipping of one strand of the hairpin (26), is observed at $Q_{n-nn}\approx$ −0.4 (see inset in A). The unfolded ensemble is located at $Q_{n-nn}\approx$ 0.1 (representative peptide structures are shown in the inset in B). The folded state (inset in C) is observed at $Q_{n-nn}\approx$ 0.7.

Free-energy calculations

From Fig. S2, we calculate the free energy of folding $\Delta F_{N-U}$ based on $Q_{n-nn}$, where

$$\Delta F_{N-U}=-k_{B}T\text{ln}\left(\frac{\underset{Q_{n-nn}^{‡}}{\overset{1}{\int }}{e}^{-\beta F\left(Q_{n-nn}\right)}d{Q}_{n-nn}}{\underset{-0.2}{\overset{Q_{n-nn}^{‡}}{\int }}{e}^{-\beta F\left(Q_{n-nn}\right)}d{Q}_{n-nn}}\right)$$ (3)

is the difference between the native $F_N$ and unfolded $F_U$ free energies, and $Q_{n-nn}^{‡}\left(=0.4\right)$ is the location of the barrier along $Q_{n-nn}$.

Results and Discussion

To characterize the folding thermodynamics in bulk and under confinement, we calculate the two-dimensional potential of mean force (PMF) as a function of two suitable reaction coordinates. The PMF plot is a convenient way to look at free energy projected onto various order parameters. Moreover, when good order parameters are used, the PMFs can be used to gain insight into a system’s thermodynamics and kinetics. Here, we use the fraction of heavy atom native contacts, $Q_{aa}$, and the fraction of native minus nonnative contacts, $Q_{n-nn}$, as two order parameters to project folding free energy onto a low-dimensional surface. A combination of $Q_{aa}$ and $Q_{n-nn}$ was found to provide a good description of the hairpin folding landscape in bulk, and the folding free-energy barrier estimated from $Q_{n-nn}$ is consistent with experimental and detailed simulation data (26).

Fig. 2 shows the folding free-energy surfaces in bulk (A) as well as under two different types of confinement (B and C). The most significant difference between the free-energy surfaces in bulk and under confinement is the complete absence of the misfolded state $\left(Q_{n-nn}\approx -0.4\right)$ under confinement. This disappearance of the misfolded basin is observed independently of the confinement size, which suggests that it results from interfacial effects, presumably due to peptide proximity near one of the walls. To rule out insufficient simulation sampling time as a cause of our observation, we also performed an REMD simulation under confinement in which all the replicas were initiated from the misfolded state structure obtained from the bulk simulation. As shown in Fig. S2 B, the misfolded state under confinement was unstable and therefore disappeared after a relatively short simulation time.

What is the rationale behind the disappearance of the misfolded basin under confinement? To address this question, we plot the density of the peptide (Fig. S1 A) and of each residue’s side-chain atoms along the z-direction (perpendicular to the walls; Fig. 3). Because of the attractive nature of the wall surface, the peptide is more likely to be found near one of the walls, as shown in Fig. S1 A. More importantly, we find that the hydrophobic side-chain atoms of residues TRP3, TYR5, PHE12, and VAL14 are mostly found near the walls as opposed to other polar and neutral residues. Vaitheeswaran and Thirumalai (35) observed a similar preference for hydrophobic side chains to stay near the surface in hydrophobic nanopores, and found it to be related to the peptide’s stability under confinement. Therefore, configurations with hydrophobic residues on the same side near a wall are preferred due to the favorable association of hydrophobic residues with the wall, and hence the misfolded state, with hydrophobic residues on the opposite side of the backbone, is avoided. We also ran a control simulation in which the peptide-wall interactions were made repulsive (achieved by eliminating the second term in Eq. 1) but all other parameters were the same as in the attractive-wall simulation for a confinement size of 1.8 nm. As shown in Fig. S4, the misfolded state in this case is still populated as in bulk. This provides further evidence in favor of our reasoning that the misfolded state in the case of attractive walls is eliminated due to preferential interactions with hydrophobic side chains.

Figure 3.

Protein side-chain number density profile (normalized by number of side-chain atoms) normal to the confining walls. The left wall is located at $z=0$ nm and the right wall is located at $z=1.8$ or 2.4 nm (shown by dashed vertical lines). Note that the slight asymmetry results only from statistical error.

Such a simple mechanism may also be plausible in the case of chaperonin function, as misfolded states appear as traps with nonnative arrangement of hydrophobic residues. Thus, in addition to providing an inert cage (and thereby preventing protein aggregation), protein-chaperonin wall interactions may also facilitate the correct formation of hydrophobic contacts and thus protein folding. In addition, some of the misfolded states may be depopulated within a chaperonin cavity due to these specific protein-chaperonin wall interactions. Our observations here therefore provide support for the hypothesis that confinement can prevent the population of kinetically trapped misfolded states, with the caveat that chaperone systems are more complicated than the one considered here.

As a secondary effect, we find that attractive confinement destabilizes the folded state with respect to the unfolded state. The folding free energy $\Delta F_{\text{N}-\text{U}}$, based on one-dimensional reaction coordinate $Q_{n-nn}$, is −0.43 kcal/mol in bulk. Under confinement, $\Delta F_{\text{N}-\text{U}}=-0.08$ and 0.74 kcal/mol for wall separations of 1.8 and 2.4 nm, respectively. The unfolded-state stabilization near an attractive wall is expected because larger protein conformations can interact favorably with the wall surface as compared with the compact folded state. We expect this effect to be stronger in the case of longer proteins because the size ratio of unfolded to folded state increases, although in this case the initial stability of the folded state (in bulk) is greater.

Conclusions

In conclusion, we have carried out extensive molecular simulations of the GB1 hairpin using an explicit solvent model in bulk solution as well as confined between planar attractive walls. We find that a misfolded state, which is otherwise observed in bulk, is completely absent under confinement. We show that hydrophobic residues tend to populate the region near the walls, thereby avoiding the misfolded state. Although our study is based on a confinement model that is very simple in comparison with biological systems, our work may shed some light on the role of interactions between the protein and confining walls in modifying a protein’s folding landscape by eliminating trapped states.