Hydrophobic association of α-helices, steric dewetting, and enthalpic barriers to protein folding

Abstract

Efficient protein folding implies a microscopic funnel-like multidimensional free-energy landscape. Macroscopically, conformational entropy reduction can manifest itself as part of an empirical barrier in the traditional view of folding, but experiments show that such barriers can also entail significant unfavorable enthalpy changes. This observation raises the puzzling possibility, irrespective of conformational entropy, that individual microscopic folding trajectories may encounter large uphill moves and thus the multidimensional free-energy landscape may not be funnel-like. Here, we investigate how nanoscale hydrophobic interactions might underpin this salient enthalpic effect in biomolecular assembly by computer simulations of the association of two preformed polyalanine or polyleucine helices in water. We observe a high, positive enthalpic signature at room temperature when the helix separation is less than a single layer of water molecules. Remarkably, this unfavorable enthalpy change, with a parallel increase in void volume, is largely compensated for by a concomitant increase in solvent entropy, netting only a small or nonexistent microscopic free-energy barrier. Thus, our findings suggest that high enthalpic folding barriers can be consistent with a funnel picture of folding and are mainly a desolvation phenomenon indicative of a cooperative mechanism of simultaneous formation of multiple side-chain contacts at the rate-limiting step.

Generic properties of folding kinetics of proteins can offer deep insights into their solvent-mediated energetics. Because many ostensibly mundane features of the folding process are not well accounted for by common notions, critical examination of their biophysical basis has proven to be a productive route to fundamental advances. A prime example is the correlation between folding rate and native topology (1, 2) and the possible connection of this behavior to folding cooperativity and specific forms of many-body intraprotein interactions (3).

When folding is formulated in terms of a multidimensional free-energy landscape, the “vertical” axis denotes the potential of mean force (PMF) of the protein, whereas all of the other dimensions represent the protein's conformational degrees of freedom. For a protein to be able to fold, the landscape surface (4) is necessarily funnel-like (5) because conformational search has to be directed to circumvent the Levinthal paradox (6, 7). This picture is readily reconcilable with the empirical folding barriers along one-dimensional free-energy profiles in traditional macroscopic descriptions (8) if the barriers arose solely from a reduction in conformational entropy during folding, because restriction on conformational freedom appears, by definition, as decrease in multidimensional surface area, rather than as barriers, on the microscopic free-energy landscape (6, 9). However, experiments indicate a significant enthalpic component in empirical folding barriers (10–14). Our interest in high enthalpic folding barriers is motivated by two physical questions: (i) How does the existence of these barriers impact the folding funnel concept? (ii) What can these barriers tell us about folding mechanisms (15)?

To address these questions, we study solvent-mediated solute–solute interactions as mimics of the interactions between different parts of a protein. The interaction free energies we consider model contributions to a protein's PMF that are represented by the vertical axis of the microscopic multidimensional free-energy landscape. PMFs have temperature-dependent enthalpic and entropic components, because solvent degrees of freedom are averaged. Here, we investigate what physical processes during folding may give rise to a significant increase in a PMF's enthalpic component. As our focus is on enthalpic barriers, we do not consider conformational entropy of the protein main chain (backbone). For this purpose, the scope of the present study is restricted to solutes that are essentially rigid with respect to main-chain conformation. Hence the entropic components of the PMFs we computed originate largely from the solvent.

Atomic simulations of PMFs and other solvation effects are extremely useful for dissecting and rationalizing protein thermodynamic data (16, 17). However, the relationship between the behaviors of small solutes (18) and larger-length-scale biomolecular assembly is not always straightforward. Notably, whereas the heat capacity of the protein folding transition state is typically lower than that of the unfolded state (11, 12), atomic simulations indicate that the heat capacity at the desolvation barrier of a pair of small nonpolar solutes is higher than that when the pair is far apart (19, 20). These conflicting trends imply that the folding transition-state heat capacity cannot be understood as a simple summation of pairwise contributions from contacts between small-solute-like chemical groups (3). Nonadditivity is prevalent in many aspects of hydrophobicity (21), consistent with recent studies pointing to significant differences in the molecular basis of hydrophobicity at small- and large-length scales (22–29). Therefore, based on this discrimination, we stipulate that an in-depth analysis of the macroscopic thermodynamic signatures of folding kinetics could yield crucial information about the length scale and many-body nature of the microscopic solvent-mediated interactions involved in the transition state.

Results and Discussion

Pursuing this investigative logic, we address whether high enthalpic folding barriers signify large length scale (in contrast to small-solute-like) desolvation at the rate-limiting step by molecular simulations of two preformed polyalanine (A₂₀) and two polyleucine (L₂₀) α-helices in a fixed relative orientation in water (Fig. 1). Calculating the separation-dependent free energy at multiple temperatures allows us to obtain the entropy, enthalpy, and heat capacity (see Methods).

Fig. 1.

Overview of the simulated system. (A) One helix (blue) is fixed, and the other helix (red) is free to move in the direction of the double arrows. The dashed lines show the simulation box. This snapshot displays the maximum helix–helix separation of 2.4 nm. (B) A view showing the fixed helix–helix crossing angle. (C) Helix–helix packing for L₂₀ at contact (r = 0.90 nm). The surfaces are solvent-accessible surfaces for a water-like spherical probe of radius 0.14 nm. The side chains are shown as cyan (carbon) and white (hydrogen) sticks.

Enthalpy–Entropy Compensation and Heat Capacity.

Fig. 2 A and F shows that the helices in the A₂₀ and L₂₀ two-helix systems prefer to be in contact at 300 K. Because of the larger leucine side chains, the contact free-energy minimum is at a larger separation and the well is deeper and broader for L₂₀. As expected for the hydrophobic effect near room temperature (16, 17), the systems display a favorable entropy change at contact. A prominent enthalpic barrier with a maximum ΔH₀ ≈ +60 kJ·mol⁻¹ at 300 K is observed for both A₂₀ and L₂₀ inFig. 2 A and F at separations slightly larger than that at contact (red curves), but the large and unfavorable enthalpy change in this region is almost completely compensated for by a favorable entropy increase (green curves). The net result is only a small desolvation free-energy barrier for A₂₀ (ΔG ≈ +8 kJ·mol⁻¹) and no free-energy barrier at all for L₂₀ (Fig. 2 A and F, black curves).

Fig. 2.

Energetics of the A₂₀ (Left) and L₂₀ (Right) dimers. Thermodynamic and geometric properties are computed as functions of the spatial separation r between the centers of mass of the helices (horizontal axes). Changes in value of the following properties (per mole of helix dimer), relative to those at large r, are plotted to characterize the association of each helix dimer. (A and F) Free-energy ΔG, i.e., PMF (black), enthalpy ΔH₀ (red), and entropic free-energy −T ΔS₀ (green) at 300 K. To facilitate comparisons, positions of the contact free-energy minimum, the desolvation barrier, and the solvent-separated minimum for each of the two helix dimer systems are marked by vertical dashed lines. (B and G) Heat capacity ΔC_P. Error bars along the ΔH₀, −T ΔS₀, and ΔC_P traces represent the standard error calculated as described in Methods. (C and H) Components of the total potential energy. Selected contributions from Lennard–Jones (dotted curves), electrostatic (dashed curves), and the sum of Lennard–Jones and electrostatic (solid curves) terms of helix–helix (red), helix–water (orange), water–water (blue), and all (black) interactions are shown by separate curves. (D and I) Change in the total number of hydrogen bonds, defined by a distance <0.35 nm between the hydrogen and an acceptor, and with a donor–hydrogen–acceptor angle <60°. (E and J) SASA (red) and MSA (black).

The heat capacity change ΔC_P is negative at contact and also at the enthalpic barrier for both A₂₀ and L₂₀ (Fig. 2 B and G). However, ΔC_P is positive for some larger helix separations. This trend is somewhat similar to the association of small nonpolar solutes (19, 20), but there is an important qualitative difference: The ΔC_P peak for A₂₀ is at a separation larger than that of the desolvation free-energy barrier, rather than coinciding with the barrier as for small nonpolar solutes (19–21).

Void Volumes Lead to Enthalpic Barriers to Helix–Helix Association.

The origin of the enthalpic barrier is clear upon a dissection of the potential energies. As the two helices approach each other, the helix–water interaction energy rapidly becomes unfavorable (Fig. 2 C and H, orange curves). In contrast, the helix–helix (Fig. 2 C and H, red curves) and water–water (Fig. 2 C and H, blue curves) interactions are becoming favorable, but more gradually. This combination leads to a peak in total interaction energy (Fig. 2 C and H, black curves) at an intermediate separation between the helices.

Fig. 3 A and B shows an excellent correlation between the total volume and enthalpy changes in the system. Local water density is sensitive to helix configuration (Fig. 3 C–H). Notably, Fig. 3D and G shows a void volume (central dark blue region) between the helices at the desolvation free-energy barrier, because water molecules cannot fit in the small intervening space when the helices are not well packed against each other at this separation. A void volume implies a reduction in water–water interactions. In this light, it is clear that at least part of the enthalpic barrier originates from less favorable direct helix–helix and helix–water interactions relative to that when the two helices are, respectively, in tighter contact or farther apart.

Fig. 3.

Changes in volume and local water density during helix association. (A and B) Change in total volume ΔV (black) and enthalpy ΔH₀ (red) for the A₂₀ (A) and L₂₀ (B) systems at 300 K. The positions of the contact minimum, desolvation barrier, and solvent-separated minimum configurations are marked by vertical lines, with labels corresponding to C–H showing the occupancy (local density) of water in a 0.05-nm slice passing through the center of mass of the two helices in these configurations. Molecular graphics were produced by using VMD (57).

Theoretical considerations (22) stipulated that a drying or dewetting transition is possible for extended nonpolar plates at separations corresponding to multiple layers of water molecules. In contrast, Fig. 3 indicates only steric dewetting in helix dimerization. A single layer of water between the helices (Fig. 3 E and H) appears to be stable on the time scale of our simulations. This trend is consistent with recent investigations (23, 25, 27, 29). For instance, a study of the collapse of the two-domain protein BhpC showed minimal dewetting until the onset of steric dewetting (23). A subsequent study of the hydrophobic collapse of a melittin tetramer revealed clear dewetting at separations corresponding to three or four layers of water (27), but the region that undergoes dewetting in this case is tube shaped, which is unlike the open space between two helices that is more accessible to stabilizing hydrogen bonding from bulk water.

Side-Chain Size Effects on Helix–Helix Desolvation Energetics.

The nature of hydrophobicity in general can differ significantly for small and large nonpolar solutes (30–32). At room temperature, the hydration free energy of short linear alkanes is proportional to the solvent-accessible surface area (SASA; see below) (33) with an effective surface tension of ≈10.5 kJ·mol⁻¹·nm⁻², whereas the surface tension for macroscopic water–oil interfaces is ≈31.4 kJ·mol⁻¹·nm⁻² (32). The crossover between a regime in which hydrogen bonding in water is hindered yet persists near the solute and one with depleted hydrogen bonding (31) was predicted to occur at a nanometer solute length scale (22, 34).

Here, upon helix dimerization, the number of water–water hydrogen bonds increases by approximately five for L₂₀ (Fig. 2I), whereas there is no increase for A₂₀ (Fig. 2D). This finding is in line with the much more favorable enthalpy at contact for L₂₀ (red curve in Fig. 2F), driven mainly by favorable changes in water–water electrostatic interactions (blue dashed curves in Fig. 2H). This trend is consistent with the consensus that water can accommodate small nonpolar solutes without significant disruption to its hydrogen-bond network, whereas it cannot do so for large nonpolar solutes and hence some hydrogen bonds have to be lost (22, 30–32, 34).

Our α-helix dimerization thermodynamics fits in a general pattern of behavior of nanoscale hydrophobic solutes (i.e., with nanometer length scale). Several features we discover are quite similar to those observed recently in simulations of nonpeptide solutes. For example, the desolvation free-energy barriers for a pair of C₆₀ fullerenes and a pair of C₆₀H₆₀ fulleranes at 298 K were found to be also quite low at ≈4 kJ·mol⁻¹ and ≈12 kJ·mol⁻¹, respectively (26). A high desolvation enthalpic barrier of ≈500 kJ·mol⁻¹at 298 K was detected in a recent two-temperature study of the association of two parallel nonpolar plates of dimensions ≈ 1.1 × 1.2 nm² (60 carbon atoms each). Similar to the entropy–enthalpy compensation we ascertain for two α-helices, the positive enthalpy change for the nonpolar plates is almost completely compensated for by a favorable entropy change such that the resultant free-energy barrier is insignificant (29).

Comparing Atomistic and Implicit Solvent Treatments: Insights and Limitations.

Can simple notions of hydrophobicity capture the intricacy of nanoscale desolvation? Fig. 2 E and J shows the variation of total SASA and molecular surface area (MSA) of the helices as they approach each other. SASA of a molecule is the area of the surface traced by the center of a spherical water probe rolling on the van der Waals surface of the given molecule (see Fig. 1), whereas MSA is the area generated by the part of probe surface facing the given molecule (35).

By construction, SASA measures the number of water molecules that can fit around the solutes; it decreases monotonically as r decreases. Comparing Fig. 2 A and F with Fig. 2 E and J indicates that the SASA trend is similar to that of entropy, consistent with the notion that reduction in water entropy is roughly proportional to the number of water molecules contacting the solutes. On the other hand, MSA is a better measure of water–solute contact, hence it is more suited for solvation enthalpy and related effects (36). Consistent with this expectation, the MSA profiles display peaks similar to the enthalpic barriers in Fig. 2 A and F that arise mainly from uncompensated losses of favorable water–solute interactions (Fig. 2 C and H). Here, the position of the MSA peak matches that of the enthalpic barrier accurately for A₂₀, but not so for L₂₀, likely because the present MSA treatment does not account for side-chain flexibility. These comparisons indicate that while “implicit-solvent” area measures such SASA and MSA can provide valuable physical insights (17, 35), perhaps no single area measure can provide adequate predictions for the spatial dependence of a broad range of thermodynamic signatures of hydrophobic association (19, 21).

Fitting ΔG at the contact minima in Fig. 2 A and F to the corresponding SASA changes in Fig. 2 E and J yields surface tensions of 11.2 and 13.6 kJ·mol⁻¹·nm⁻², respectively, for A₂₀ and L₂₀. Both values are far from the macroscopic limit of ≈30 kJ·mol⁻¹·nm⁻² (see above); nonetheless, the effective surface tension for L₂₀ is ≈20% higher than that for A₂₀. Thus, consistent with its larger size, the behavior of L₂₀ is slightly more macroscopic-like than that of A₂₀. The negative ΔC_P at contact is larger for L₂₀than for A₂₀ (Fig. 2 B and G); this difference follows from L₂₀'s larger decrease in surface area upon contact (Fig. 2 E and J) and that the ΔC_P per SASA decrease is approximately twice as large for L₂₀ as for A₂₀ (−0.14 versus −0.07 kJ·mol⁻¹·K⁻¹·nm⁻²).

Helix–Helix Association Thermodynamics and Water Distribution.

Fig. 3 C–H examines the distribution of water around the helices. When the helices are in contact, there is tight packing and interdigitation of side chains along the helix–helix interface (Fig. 3 C and F). When the helices are a little apart, Fig. 3 D and G shows the development of a void volume, i.e., steric dewetting, that leads to a high enthalpic desolvation barrier (see above).

For A₂₀, a relatively shallow (≈ −5 kJ·mol⁻¹) solvent-separated free-energy minimum is observed at separations slightly larger than that at the desolvation barrier (Fig. 2A). The absence of a corresponding solvent-separated ΔG minimum for L₂₀is likely caused by the tendency of the flexible leucine side chains to smooth out subtle features. At the solvent-separated minimum of A₂₀, the local density plot (Fig. 3E) shows that in between the two helices there are individual water molecules with occupancy much higher than bulk, suggesting that they are localized. Thus, the favorable enthalpy in this region likely results from the packing of the two helices with a layer of water molecules fitting tightly in between. In contrast, at the corresponding separation for L₂₀ (Fig. 3H), the water between the two helices displays occupancy closer to the bulk value, suggesting that the water molecules are less confined. For the less flexible A₂₀system, an additional free-energy barrier (second maximum at r ≈1.30 nm) and an additional free-energy minimum (at r ≈1.46 nm) can be discerned, echoing a similar, but more dramatic, pattern observed in simulations of two smooth hydrophobic surfaces (25).

Ramifications for the Transition States of Protein Folding.

The results above on nanoscale hydrophobic interactions provide perspectives on the critical role of water (37–41) and the nature of transition states (42, 43) in protein folding and help resolve at least two puzzles. First, as stated above, the change in heat capacity ΔC_P from the unfolded to transition state is usually negative, but the ΔC_P trend for small nonpolar solutes such as methane is opposite (19–21), indicating basic physical differences between the two processes. Now, in view of the negative ΔC_P at the desolvation barrier for a pair of helices (Fig. 2 B and G), protein unfolded-to-transition state ΔC_P may be rationalized, at least in part, by desolvation of nanoscale hydrophobic surfaces.

Second, although simulations of small nonpolar solutes have revealed a compensation between enthalpy and solvent entropy at the desolvation barrier, the height of the enthalpic desolvation barrier of small solutes is too small to account for the much higher enthalpic protein folding barriers. For example, at 25°C, the enthalpic folding barrier ΔH^‡−D (in the original notation) ≈30 kJ·mol⁻¹ for chymotrypsin inhibitor 2 (CI2) (11) and ≈32 kJ·mol⁻¹ for cold shock protein CspB (12); but the enthalpy peak is only ≈7.5 kJ·mol⁻¹ for three-methane association at room temperature (21). A recent simulation of protein A (38) found that the enthalpy change from an unfolded to a transition regime is negative at the transition temperature, consistent with experiment (14), but conditions corresponding to lower experimental temperatures with positive enthalpic folding barriers were not explored. Here, Fig. 2 A and F shows that the ≈+60 kJ·mol⁻¹ enthalpic barrier for helix dimerization is comparable and can be even higher than that for protein folding at 300 K. For L₂₀, the ΔC_P around the desolvation barrier is also similar to the ΔC_P^‡-D ≈ −1.3 kJ·mol⁻¹·K⁻¹ reported for CI2 (11). All in all, the desolvation of the L₂₀ dimer displays thermodynamic signatures that are qualitatively and quantitatively similar to the folding transition states of small two-state proteins.

In our two-helix systems, the unfavorable enthalpy increase at desolvation is concomitant with a favorable solvent entropy increase as water is released from the interhelix interface. Consequently, there is no free-energy barrier for L₂₀ and the free-energy barrier is much lower than the enthalpic barrier for A₂₀. These dramatic compensations lend credence to the idea that the unfavorable enthalpic signature of the folding transition state does not necessarily contradict the funnel picture of the microscopic free-energy landscape (15), which allows for low barriers on mildly rugged, overall downhill slopes (6, 7). By the same token, the heights of experimental enthalpic folding barriers, which significantly exceed the enthalpic barriers of small-solute association, may be viewed as evidence that the folding rate-limiting step generally involves desolvating many side chains in a cooperative, essentially simultaneous manner. In this perspective, it is noteworthy that the enthalpic folding barriers of some proteins are lower than the enthalpic desolvation barriers for A₂₀ and L₂₀ (see above). This finding suggests that, for these proteins, the degree of cooperativity in simultaneous side-chain desolvation at the folding rate-limiting step could be somewhat lower than that in the present helix dimerization models.

Outlook

This study is based on models with fixed main-chain helical conformations that are designed to explore transient nanoscale events at the folding rate-limiting step. The above analysis underscores how length-scale dependence of solvent-mediated effects in conjunction with macroscopic thermodynamic data may be used to provide microscopic energetic and structural information about the folding transition state. Our results rationalize several generic, yet puzzling, phenomena in folding kinetics; they also raise intriguing questions. For instance, while our approach is suggestive of collective dynamics similar to that in the “diffusion-collision” model (44), our helix dimerization model does not address the stability of isolated helices because their unfolding is precluded. Therefore, results reported here can also be consistent with a folding scenario in which the cooperative formation of multiple side-chain contacts occurs between extremely transient helices. To tackle a broader range of folding questions, studies with more relaxed conformational restrictions will be necessary to explore, for example, a possible cooperative interplay between local structural propensity and nonlocal contacts (3).

Methods

The starting structures were generated by simulated annealing (45). Both of the two-helix starting structures adopt a coiled-coil antiparallel geometry with a crossing angle θ ≈ −27° for A₂₀ and +28° for L₂₀. One helix was fixed in space by harmonic restraints on the α-carbons; the other helix had restraints applied in only two dimensions (hence the helical conformation and θ were fixed) and was free to slide along the helix–helix vector to vary the separation r (Fig. 1). The side chains and water molecules were not restrained. The helices were placed in a rectangular box of ≈6 × 4.5 × 4.5 nm³, and solvated with 3,867 and 3,778 water molecules, respectively, for A₂₀ and L₂₀. Simulations were performed under essentially atmospheric pressure (1 bar = 0.987 atm) at five temperatures ranging from T = 275 to 350 K, using the GROMACS software package (46), the OPLS all-atom force field (47, 48), the TIP3P water model (49), and a time step of 2 fs. Bonds were constrained to their equilibrium lengths by the SETTLE algorithm (50) for water and the LINCS algorithm (51) for other molecules. The Lennard–Jones interactions were evaluated by using a 0.9/1.4-nm twin-range cutoff. Electrostatic interactions were evaluated by using the smooth particle mesh Ewald algorithm (52, 53) with 0.9-nm real space cutoff, 0.12-nm Fourier spacing, and tinfoil boundary conditions. An umbrella sampling protocol was used to sample in the range of r = 0.64 to 2.4 nm for A₂₀ and 0.8 to 2.4 nm for L₂₀, using a harmonic biasing potential with a spacing of 0.1 nm and a force constant of 3,000 kJ·mol⁻¹·nm⁻². The results were unbiased with the weighted histogram analysis method (54). The simulations were performed as part of the Canadian Internetworked Scientific Supercomputer Project in essentially 1 day on all academic supercomputers in Canada (55). For each r at a given T, 6 ns of molecular dynamics was simulated, with data from the first 1 ns discarded to ensure equilibration. The remaining 5 ns was split into five 1-ns blocks, which were treated independently on the basis of rapid fluctuations in r and in water density (data not shown). A total of 3.2 μs of simulation time was collected.

PMFs of helix–helix association at several Ts are shown in supporting information (SI) Fig. 4. The heat capacity function was obtained by linear fit to the equation:

where ΔU(T, r) is the change in total potential energy at T, from a large helix–helix separation of 2.4 nm to separation r. The enthalpy and entropy at T = T₀ were then obtained by fitting to the standard relation:

with ΔC_P(r) held fixed at the value obtained from Eq. 1, and T₀ chosen to be 300 K. Fits were performed by Mathematica 5.1 from Wolfram Research, (Champaign, IL) using the Regress and NonlinearRegress functions. Standard errors were obtained by treating each 1-ns block as an independent sample and taking the asymptotic standard error (as returned by NonlinearRegress).

As a consistency check, we also computed ΔH₀ directly from the potential energies; the results are in good agreement with Eq. 2 (SI Fig. 5). To assess robustness of our results across different force fields, as has been ascertained for small nonpolar solutes (20), we repeated the PMF and volume calculations for L₂₀ by using the GROMOS ffG53a5 force field (56). The similarity of the predictions from the two force fields (SI Fig. 6 and SI Fig. 7) provides evidence that our results are representative of general physical trends in nanoscale hydrophobic interactions.

Abbreviations

PMF

potential of mean force

SASA

solvent-accessible surface area

MSA

molecular surface area.