Unfolding of Hydrophobic Polymers in Guanidinium Chloride Solutions

Jan 26, 2010 - Rahul Godawat, Sumanth N. Jamadagni, and Shekhar Garde*. The Howard P. Isermann Department of Chemical & Biological Engineering, ...
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J. Phys. Chem. B 2010, 114, 2246–2254

Unfolding of Hydrophobic Polymers in Guanidinium Chloride Solutions Rahul Godawat, Sumanth N. Jamadagni, and Shekhar Garde* The Howard P. Isermann Department of Chemical & Biological Engineering, and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, New York 12180 ReceiVed: July 22, 2009; ReVised Manuscript ReceiVed: NoVember 19, 2009

Guanidinium chloride (GdmCl) is a widely used chemical denaturant that unfolds proteins. Its effects on hydrophobic interactions are, however, not fully understood. We quantify the effects of GdmCl on various manifestations of hydrophobicity s from solvation and interactions of small solutes to folding-unfolding of hydrophobic polymers s in water and in concentrated GdmCl solutions. For comparison, we also perform similar calculations in solutions of NaCl and CsCl in water. Like NaCl and CsCl, GdmCl increases the surface tension of water, decreases the solubility of small hydrophobic solutes, and enhances the strength of hydrophobic interactions at the pair level. However, unlike NaCl and CsCl, GdmCl destabilizes folded states of hydrophobic polymers. We show that Gdm+ ions preferentially coat the hydrophobic polymer, and it is the direct van der Waals interaction between Gdm+ ions and the polymer that contributes to the destabilization of folded states. Interestingly, the temperature dependence of the free energy of unfolding of the hydrophobic polymer in water is protein-like, with signatures of both heat and cold denaturation. Addition of GdmCl shifts the cold denaturation temperature higher, into the experimentally accessible region. Finally, translational as well as conformational dynamics of the polymer are slower in GdmCl and correlate with dynamics of water molecules in solution. I. Introduction Guanidinium chloride (GdmCl) and urea are widely used at high concentrations (g5 M) to denature proteins. Experimental1-6 as well as modeling and simulation studies7-11 have focused on understanding the role of denaturants in protein unfolding. Two mechanisms have been discussedsan indirect mechanism in which the action occurs through changes in water structure and a direct one in which interaction of denaturants with the backbone and side chains plays the dominant role. The concept of an “indirect mechanism” appears to us to be ill-defined and difficult to quantify. Specifically, arguments based on “enhanced” or “decreased” water structure can not be translated into thermodynamic equations via a molecular theory and are therefore of limited utility. Several studies have pointed to the “direct mechanism” being responsible for denaturation, with the details of denaturant-backbone, direct hydrogen bonding, and interactions with hydrophobic side chains currently being quantified.4,7,12-15 Recent work by Hua et al.10 and Zangi et al.16 highlights the importance of dispersion interaction between urea and a protein/ polymer in unfolding the protein Lysozyme or a hydrophobic polymer, respectively. In a commentary on the work of Hua et al.,10 Rossky raises several important questions17 about the generality of observations made for urea. Does the guanidinium ion act through a similar mechanism? Given that the guanidinium ion is bulky and weakly hydrated, does it associate with hydrophobic groups in solution? Although association of the guanidine group with certain specific binding pockets is known, its effect on hydrophobic interactions is not well understood. One reason could be that that experimental studies have focused on protein-urea/GdmCl solutions4,13 where it is difficult to isolate hydrophobic effects due to the chemical heterogeneity * Author to whom correspondence should be addressed. E-mail: [email protected].

of a protein. Simulation studies,8-10 in the same spirit, have also focused on protein systems and have provided information about solution structure (e.g., radial distribution functions and hydrogen bond analysis10,15) and enthalpic interactions.10 However, due to the large system sizes, and associated computational expense, calculation of the free energy of unfolding, its temperature dependence, or its resolution into different contributions is difficult to achieve. In the small solute regime, O’Brien et al.7 have calculated the potential of mean force (PMF) of methanes in pure water and GdmCl solutions using MD simulations. While a strengthening of the contact minimum in the PMF was observed, they interpret it as not being significant. At larger length scales, Gunari et al.18 report studies of unfolding of a hydrophobic polystyrene chain by pulling it in an atomic force microscope (AFM) experiment. In water, which is a poor solvent, the polystyrene chain collapses. Correspondingly, the force vs extension curves show a distinctive plateau in water, but not in a good solvent like toluene. Interestingly, a similar good-solventlike behavior is observed in aqueous GdmCl solutions. Gunari et al. interpret that result as evidence for weakening of hydrophobic interactions in GdmCl solution. One may find this weakening somewhat surprising given that GdmCl addition increases the surface tension of water.19 In a recent communication, England et al.20 show that both urea and GdmCl stabilize the liquid phase of water in the region confined between two hydrophobic plates, thereby preventing the onset of dewetting, which again may be interpreted as suggesting weakening of hydrophobic interactions. Guanidinium (Gdm+), C(NH2)3+, is a planar, bulky, and monovalent cation with low overall charge density and lies at one end of the Hofmeister series.21 The hydration of Gdm+ and the structure of concentrated GdmCl solutions have been extensively studied using neutron diffraction22 and MD simulations.23 Those studies indicate a bimodal hydration of Gdm+

10.1021/jp906976q  2010 American Chemical Society Published on Web 01/26/2010

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TABLE 1: Force-Field Parameters Used in MD Simulations molecule watera guanidiniumb TMAc ionsd methanee polymerf

atom type

σ, nm

ε, kJ/mol

q, e

OW HW C N H NT CT Na Cs Cl ME PC

0.3169 0 0.2250 0.3250 0 0.3800 0.3960 0.2583 0.3883 0.4401 0.3730 0.4400

0.6502 0 0.2092 0.7113 0 0.2090 0.6070 0.4185 0.4185 0.4185 1.2340 0.8500

-0.8476 +0.4238 +0.64 -0.80 +0.46 0.00 +0.25 +1.00 +1.00 -1.00 0.00 0.00

a SPC/E model of water.30 b OPLS model31 for the guanidinium ion (the parameters are similar to the guanidinium group in arginine in AMBER and have been extensively used in the literature for GdmCl simulations, e.g., in refs 7 and 23). c Tetramethyl ammonium ion model from Garde et al.32 d From refs 33 and 34. e From ref 35. f From ref 36.

with N-H groups making well-ordered hydrogen bonds in the molecular plane and the planar faces being weakly hydrated.23 The tendency of Gdm+ ions to stack parallel to their molecular plane in GdmCl solutions suggests their ability to interact favorably with both water and hydrophobic side chains simultaneously. Here, we quantify the effects of GdmCl on various manifestations of hydrophobicityssmall solute solvation, their pair interactions, vapor-liquid surface tension, and folding and unfolding of a hydrophobic polymer in water. We perform similar studies in NaCl, CsCl, and TMACl (TMA ) tetramethyl ammonium) solutions to compare and contrast the effects of these different salts with a common anion. We find that for small solutes where attractive interactions with Gdm+ are weak GdmCl enhances the strength of hydrophobic interactions somewhat. In contrast, for a hydrophobic polymer with alkanelike dispersive interactions, GdmCl-polymer attractions dominate. Gdm+ ions coat the polymer with their planes parallel to the polymer surface, thus destabilizing folded states. Such behavior is not observed in NaCl, CsCl, or TMACl solutions. These differences between effects of GdmCl and other salts highlight the importance of Gdm+ ion chemistry and shape (planarity) in unfolding hydrophobic polymers. We show that the hydrophobic polymer displays signatures of both heat and cold denaturation, and the addition of GdmCl increases the cold denaturation temperature. We also comment on the dynamics of hydrophobic collapse in salt solutions and its coupling with solvent dynamics. II. Methods We quantified (i) the hydration of small hard-sphere solutes, (ii) interactions of small hydrophobic solutes (methanes), and (iii) folding-unfolding of a hydrophobic polymer in water and in GdmCl solution as well as in aqueous solutions of simple salts, NaCl and CsCl. Since GdmCl is typically used at high concentrations, we simulated 4.9 M solutions of all salts. The Gdm+ ion is a multisite cation, with low overall charge density. For comparison, we therefore performed simulations of the hydrophobic polymer in 4.9 M tetramethyl ammonium chloride (TMACl) solution. The total number of water molecules in simulations ranged from 3200 to 3400, and ion pairs ranged from 355 (NaCl), 400 (CsCl), 446 (GdmCl) to 520 (TMACl) (see Table 1 for force-field details). Lorentz-Berthelot rules24

were used to calculate cross interactions. The simulation box was roughly 5 × 5 × 5 nm3 with 3D-periodic boundary conditions. Small Solute Hydration and Interactions. We calculated the probability of successful insertion of hard-sphere solutes of different radii in salt solutions to obtain the free energy of hydrophobic hydration.26 Equivalent hard-sphere radii of various heavy atom sites were defined using the protocol used by Hummer et al.25 and Kalra et al.26 15 625 insertions were done per configuration in 7500 configurations from a 7.5 ns long trajectory for each solution. To quantify hydrophobic interactions at the pair level, we performed simulations of methane-like Lennard-Jones solutes in water and in the additive solutions. Methane-methane pair correlations, g(r), were calculated, and the potential of mean force (PMF) between two methanes is then given by27 WMe-Me(r) ) -kT ln[g(r)]. The effects of additives on hydrophobicity are frequently related to their effect on the surface tension of water. Qualitatively, if the additive increases the surface tension, then, it will also oppose creation of hydrophobic interfaces, thereby strengthening hydrophobic interactions, and vice versa. An inherent assumption is that the interface of hydrophobic solutes with water is like a vapor-liquid interface of water, and further, the interactions between the additive and hydrophobic solutes are negligible (as is the case when the hydrophobic solute is an idealized hard-particle solute). To test these ideas, we calculated the surface tension of pure water and of the additive solutions. We increased the z dimension of the simulation box to ∼12 nm, thus creating a liquid slab with two liquid-vapor interfaces. Surface tensions were calculated by integrating the difference between the normal and lateral components of the pressure tensor (eq 129) obtained from 8 ns long simulations.

γ)

Lz 1 〈P 〉 - (〈Pxx〉 + 〈Pyy〉) 2 zz 2

[

]

(1)

Polymer Simulations. To quantify how GdmCl affects manybody hydrophobic interactions relevant to folding-unfolding, we studied conformational equilibrium, structure, and dynamics of a hydrophobic 25-mer (denoted as CG25-LJ by Athawale et al.36) in water and in additive solutions. The polymer is a freely jointed 25-mer of Lennard-Jones solutes (see Table 1 for parameters) with harmonic bond potentials (Ubond ) (1/2)kb(l - l0)2, where kb ) 60 702 kJ/mol/nm2 and l0 ) 0.25 nm). In the extended state, the polymer is ∼5.1 nm long and roughly represents a coarse-grained version of a freely jointed C50 alkane, with each monomer representing an ethanelike unit. Umbrella sampling was performed along the radius of gyration, Rg, order parameter to calculate the conformational free-energy profile, W(Rg) (refer to Athawale et al.36 for details). Twenty separate windows (each 5 ns long) were used spanning a 0.45-1.4 nm Rg window, sampled every 0.05 nm. To study the polymer in bulk water, it was solvated in a cubic box of length ∼5 nm (≈4100 water molecules). To study the dynamics of collapse and translational diffusion of the polymer, we performed 50 additional simulations for each system, all starting with microscopically different configurations of the polymer in an extended conformation. Starting conformations were obtained from the Rg ) 1.4 nm umbrella window, and the collapse was monitored by tracking Rg as a function of time. All simulations, except the liquid-vapor ones to calculate surface tension, were performed in the NPT ensemble at 1 atm and 300 K, maintained using a Nose-hoover thermostat37 and

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Figure 2. PMF, W(Rg), for polymer folding in water and 4.9 M GdmCl, CsCl, NaCl, and TMACl solutions at 300 K. The PMF is referenced to zero at Rg ) 1.40 nm.

Figure 1. (a) Free energy of solvation of a hard-sphere solute in water and in 4.9 M GdmCl, NaCl, and CsCl solutions at 300 K measured in MD simulations. (b) Methane-methane PMF, WMe-Me(r), in water and 4.9 M salt solutions at 300 K.

Parrinello-Rahman barostat,38 respectively. The liquid-vapor simulations were performed in the NVT ensemble. Additional simulations of the polymer in water and in 4.9 M guanidinium chloride solution were performed in the temperature range of 280-380 K to calculate the temperature dependence of the PMF, W(Rg). Electrostatics were handled using the Particle Mesh Ewald algorithm.39 All simulations were performed using GROMACS40,41 modified to perform umbrella sampling on Rg. The SHAKE algorithm was used to constrain bonds in water molecules. III. Results and Discussion A. Hydrophobic Hydration and Interactions in GdmCl Solutions. Initially, we focused on the effects of GdmCl on primitive hydrophobic effects. Figure 1a shows the free energy ex , of a hard sphere of radius, r, in water and in of insertion, µHS ex is of interest because it makes the additive solutions.26,42 µHS dominant contribution to excess chemical potentials of small ex is higher (i.e., unfavorable) hydrophobic solutes in water. µHS in all additive solutions than in pure water. It is highest in NaCl solution and is similar in CsCl and GdmCl solutions. The ex indicates reduced solubility of hard-sphere increase of µHS solutes in all additive solutions. Indeed, at room temperature, methane exhibits a lower solubility in 4.9 M GdmCl or 7 M urea solutions than in pure water.1 Both NaCl and CsCl reduce the solubility of all alkanes including methane.26,27,43,44 Interestingly, experimental1 and simulation data45,46 on the solubility of larger alkanes (n > 2) show that their transfer free-energy from water to urea and GdmCl solutions is favorable and highlight the role of alkane-solvent attractive interactions in increasing the solubility of larger alkanes in GdmCl solutions. How does the addition of GdmCl affect the interaction between two methanes in water? Figure 1b shows the Me-Me PMF in water and in different salt solutions. That typical salts increase the strength of hydrophobic interactions is wellknown,26-28,43 and correspondingly in NaCl and CsCl solutions the contact minimum becomes more favorable by about 2 kJ/ mol relative to that in pure water. Although the details of the

Me-Me PMF in GdmCl solution are slightly different, strengthening of hydrophobic interactions at the pair level is observed similar to that in NaCl solution. The relative stabilization of the Me-Me contact pair in GdmCl solutions is consistent with simulation results of O’Brien et al.7 B. Thermodynamics of Folding-Unfolding of a Hydrophobic Polymer in Water and in GdmCl Solutions. To study the effect of GdmCl on manybody hydrophobic effects, we selected a model polymersa freely jointed hydrophobic 25mer having alkane-like interactions with water. This polymer or similar long-chain alkanes47,48 and homopolymers49 serve as excellent model systems for studies of hydrophobically driven collapse50 and have been studied in detail in water,36,51 in mixed solutions,27,48,52 as well as at interfaces.53,54 In water, hydrophobic interactions drive the polymer to fold into compact, globular states over subnanosecond time scales.53 The PMF along the radius of gyration, W(Rg), calculated using umbrella sampling simulations in water and in GdmCl, NaCl, CsCl, and TMACl solutions is shown in Figure 2. We compare the results for GdmCl and TMACl and discuss their relevance separately at the end of this subsection. In water, the PMF, W(Rg), is monotonic, and compact globular states (Rg ∼ 0.55) are favored by about 28 kJ/mol over extended states. Adding NaCl or CsCl to water stabilizes folded states, increasing the depth of the minimum to about 45-50 kJ/mol, consistent with similar observations for a smaller polymer reported previously by our group.27 The differences between PMFs in NaCl and CsCl solutions highlight the role of cation size (σNa ) 0.2583, σCs ) 0.3883 nm). The smaller Na+ ions with their higher charge density are more effective stabilizers than the larger Cs+ ions.26 In contrast to NaCl or CsCl, the GdmCl solution reduces the depth of the minimum by about 6 kJ/mol. Given that results for small hydrophobic solutes at the singlet or pair level suggest stabilization of hydrophobic interactions, the above destabilization of folded states of the polymer is interesting. To understand the mechanism of GdmCl-induced destabilization, we calculated different contributions to the PMF, W(Rg). Following Athawale et al.,36 we decomposed the PMF as

W(Rg) ) Wvac(Rg) + 〈Upw(Rg)〉 + 〈Up-add(Rg)〉 + Wsol(Rg) (2) where Wvac is the PMF of the polymer in vacuum and is calculated by performing independent umbrella simulations.

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Figure 4. PMF, W(Rg), for polymer folding in water, in 4.9 M solutions of three different guanidinium chloride models, Gmd(0.5)Cl, GdmCl, and Gdm(1.5)Cl models at 300 K. The PMF is referenced to zero at Rg ) 1.40 nm. Figure 3. Different contributions to the polymer PMF, W(Rg), as defined by eq 2 at 300 K. All terms are referenced to zero at Rg ) 1.40. (a) The PMF in vacuum, Wvac(Rg). (b) Solvent contribution to PMF, Wsol(Rg). The inset shows the same over a smaller range of Rg to highlight that the differences are consistent with surface tension measurements, as indicated by the arrow in the direction of increasing surface tension of the solvents. (c) Total polymer-solution interactions, 〈Up-sol(Rg)〉 ) 〈Up-add(Rg)〉 + 〈Upw(Rg)〉. (d) Polymer-additive interaction energy, 〈Up-add(Rg)〉 in different additive solutions. The arrow indicates the enhancement in polymer-additive interactions responsible for destabilization of folded states of the polymer in GdmCl solutions. Inset shows 〈Up-add(Rg)〉 for the CsCl system scaled up by a factor of 4.5 and raw data for 〈Up-add(Rg)〉 for the GdmCl system.

〈Upw(Rg)〉 and 〈Up-add(Rg)〉 are the ensemble-averaged polymerwater and polymer-additive interaction energies, respectively, and Wsol(Rg) is the effective solvent contribution to the PMF. Such a separation has been shown to be useful in development of a perturbative treatment of the PMF.51 In that picture, Wsol(Rg) roughly quantifies the effect of the solution on a repulsive reference polymer. Alternatively, it is the so-called “cavity contribution” and quantifies the effect of solution on the behavior of a polymer-shaped cavity. Figures 3a, b, and c show Wvac, Wsol(Rg), and the total polymer-solution attractions, 〈Upw〉 + 〈Up-add〉, respectively. In vacuum, intrapolymer attractions fold the polymer into compact states. The other two terms are large and oppose each other. Because the vacuum contribution is the same in each solution, it is the balance of the other two terms that governs the behavior shown in Figure 2. Below we show that GdmClinduced destabilization of the polymer is due to attractive interactions between GdmCl molecules and the polymer. In all solutions, the solvent contribution, Wsol, greatly favors folded states (Figure 3b). This is expected as Wsol characterizes the solvent-induced driving force for a repulsive reference polymer. In the simplest surface-area-based model, Wsol(Rg) ≈ γ × A(Rg), where γ is the surface tension and A is the area of a given conformation. The surface tension is positive, and Wsol will favor more compact states. Qualitatively, the surface tension of a vapor-liquid interface of different solutions provides clues into additive-induced stabilization. Experiments as well as our calculations of surface tension indicate that additives increase γ. Consistent with other simulations,55 we find the surface tension of SPC/E water to be ∼56 mJ/m2. We calculate surface tensions of the additive solutions to be γGdmCl ∼ 59 mJ/m2, γCsCl ∼ 63 mJ/m2, and γNaCl ∼ 68 mJ/m2. The relative changes in γ are reasonable

and comparable to the corresponding experimental measureexp exp exp ments19,56 (γwater ) 72 mJ/m2, γGdmCl ) 75 mJ/m2, and γNaCl ) 2 83 mJ/m ). These values imply that the solvent contribution, Wsol(Rg), will increasingly favor folded states as the solvent changes from pure water to GdmCl to CsCl and NaCl. Indeed, Figure 3b shows that Wsol(Rg) favors folded states in the same order. The polymer-solution attractions favor unfolded states of the polymer in all solutions (Figure 3c). Interestingly, the polymer-solution energy profiles are essentially identical in water, NaCl, and CsCl solutions. The change in polymer-solution energies in GdmCl solutions is somewhat larger and further favors unfolded states. Resolution of this term into polymer-water (not shown) and polymer-additive contributions (Figure 3d) indicates that the more favorable polymer-GdmCl interactions dominate the energetics and contribute to the destabilization of the folded states. Two factors contribute to GdmCl-polymer interactions being more favorable. First, Gdm+ is a multisite ion containing four heavy atoms (one carbon and three nitrogens) that have van der Waals interactions with the polymer. Second, as we show in the next subsection, Gdm+ concentration is enhanced near the polymer. These two factors enhance the GdmCl-polymer energy by a factor of ∼4.5 compared to the other salts (Figure 3d, inset). Given that urea is a neutral multisite solute, we expect it to bind to the hydrophobic polymer leading to destabilization of folded states similar to that by GdmCl observed here. To test the sensitivity of the results obtained here to the Gdm+ force-field parameters, we performed simulations of two modified guanidinium models, in which the Lennard-Jones well depth, ε, of each site of the cation was scaled by a factor of 0.5 and 1.5, respectively. We denote these Gdm models as Gdm(0.5) and Gdm(1.5). Scaling of ε changes both the Gdm+-water and Gdm+-polymer interactions. Specifically, mixing rules scale the interactions by a factor of 0.5 ) 0.707 for Gdm(0.5) and 1.5 ) 1.22 for Gdm(1.5), respectively. The PMFs, W(Rg), in these modified guanidinium solutions are shown in Figure 4. Surprisingly, the PMFs are rather insensitive to the exact details of the force field, with folded states being destabilized by about the same amount in all cases. This can be understood as follows. The scaling of the ε value for Gdm ions changes the polymer-Gdm energy as well as properties of the water-Gdm solution (e.g., surface tension). Increasing ε makes polymer-Gdm interactions more favorable,

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leading to a bias for unfolding and vice versa. Correspondingly, increasing ε for Gdm-water interactions increases the surface tension of water-Gdm solutions: γGdm(1.5) (∼63 mJ/m2) > γGdm (∼59 mJ/m2) > γGdm(0.5) (∼54 mJ/m2), thus favoring folding of the polymer for larger ε values. Although precise a priori prediction of these opposing contributions is difficult, our calculations show that the two roughly compensate each other, leading to the insensitivity of the polymer PMF to ε (Figure 4). It is experimentally known that GdmCl increases the surface tension of water. Surface tension data and trends for Gdm and Gdm(1.5) are thus consistent with experimental trends, whereas those for Gdm(0.5) are not. Importantly, in both of these models, it is the additive-polymer attractive interactions that dominate and destabilize the folded states of the polymer. To further probe the idea that it is the multisite nature of a large cation with low overall charge density that results in destabilization of the folded states of the polymer, we performed simulations of the polymer in tetremethylammonium chloride (TMACl) solution. From the PMF (Figure 2), it is clear that TMACl, in spite of being a fairly bulky cation with five interaction sites, significantly stabilizes folded states. TMACl (4.9 M) significantly increases the surface tension of SPC/E water (∼70 mJ/m2). This large increase in the hydration contribution effectively dominates any increase in enthalpic interactions that favor unfolded states. In fact, the stabilizing effect of TMACl salts on proteins is well-known.57 These results suggest that the planarity of guanidinium (or urea) is an important structural feature of these denaturants. Mason and co-workers21 have studied another denaturant with a relatively planar face, tetrapropylammonium chloride (TPACl), and highlighted similarity of its hydration and its orientations near hydrophobic residues of proteins. TPACl actually acts as a surfactant and decreases the surface tension of water, which further helps the unfolding process. To summarize, the balance between the solvent contribution and polymer-solution attractions governs the overall behavior of the polymer in solutions. In NaCl and CsCl solutions, polymer-solution energies are unchanged from that in water, and the Wsol contribution favors folding of the polymer even more than that in water. In GdmCl solution, although the Wsol contribution similarly favors folding of the polymer, polymerGdmCl interactions more than compensate leading to an effective destabilization of folded states. C. Ion Distribution and Structure near the Polymer. Figure 5 shows snapshots of instantaneous locations of various ions in the vicinity of folded and unfolded conformations of the hydrophobic polymer. The enhancement of Gdm+ ions near the polymer is visible. Figure 5 shows a more quantitative analysis of the structure using proximal distribution functions of ions near the polymer. Technical details of “proximal” density calculations are discussed elsewhere.58-61 Like radial distribution functions, these distributions quantify ion density as a function of the distance from polymer monomers, except that the normalization volumes in the calculations account appropriately for the space around a given monomer occupied by the polymer which is not accessible to ions. Figure 6 shows that Gdm+ ion concentration is significantly enhanced near the polymer, with the first peak height indicating a local density that is over three times that in the bulk. In contrast, the smaller single site cations, Cs+ and Na+, are depleted from the vicinity of the hydrophobic polymer as indicated by local density being less than that in the bulk. Such a preferential exclusion of ions from hydrophobic solutes is wellknown.26 Figure 6 also shows that the proximal density of ions

Godawat et al.

Figure 5. Snapshots from simulations of the polymer in GdmCl and NaCl solutions. The polymer (red) and ions within 6 Å of the polymer are highlighted in spacefill. (a) and (b) Snapshots of Gdm+ (carbon, cyan; nitrogen, blue; and hydrogens, white, all spacefill) and Cl- ions (gray, spacefill) around folded (Rg ∼0.55 nm) and unfolded states (Rg ∼1.40 nm) of the polymer, respectively. (c) and (d) Snapshots of Na+ (blue, spacefill) and Cl- ions around folded and unfolded states of the polymer, respectively. The zoom level is different in different panels.

Figure 6. Proximal radial distribution functions between polymer monomers and cations, g(r), in GdmCl, CsCl, and NaCl solutions obtained for polymers in folded (F, Rg ∼ 0.55 nm) and extended (U, Rg ∼ 1.40 nm) states.

near the monomers of the polymer is the same for folded as well as unfolded states. This observation, as well as independent calculations of ion distributions surrounding an isolated hydrophobic monomer (not shown) in salt solutions, which are also similar, indicate negligible length scale dependencies of ion distributions over the range sampled here. Of course, the actual number of ions within a certain distance of the polymer will be larger in the unfolded state simply because the integration volume will be larger (i.e., unfolded states have a greater exposure). The preferential water-mediated binding or exclusion of additives to a macromolecular solute in solution is determined by the complex interplay of cross-interactions in this threecomponent system. Smaller ions with high charge density are well hydrated and are typically excluded from the vapor-liquid or hydrophobic interfaces. Larger ions with lower charge density

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are less well hydrated62 and are more likely to be interfacially active. Recent simulations by Horinek et al.63 show binding of larger halide ions to a hydrophobic surface, and Zangi et al.64 show a preferential binding of low charge density ions to a hydrophobic plate in water. Simulation studies also show binding of iodide to a hydrophobic patch on a protein surface.65 Gdm+ ions are even larger and have additional multisite van der Waals interactions with hydrophobic (or any other) surfaces which makes binding to surfaces more favorable. Detailed analysis of simulations shows that the planar faces of Gdm+ ions are weakly hydrated23 leading to parallel stacking of Gdm+ ions in concentrated solutions. Snapshots from MD simulations (Figure 5) show that Gdm+ ions coat the polymer with their planes parallel to the local polymer surface. This is consistent with simulations by England et al.,20 where they find that the Gdm+ ion binds and stays roughly parallel to flat hydrophobic plates. Such an orientation also allows Gdm+ to hydrogen bond with water or salt-bridge with a chloride ion parallel to the surface of the polymer. The enhanced density of Gdm+ ions in the polymer vicinity comes at the expense of water density in the vicinity. That is, Gdm+ ions displace water from the polymer vicinity. The loss of polymer-water interactions is, however, more than made up for by the more favorable polymer-multisite-Gdm+ ion interactions. We note that the above arguments about interfacial activity of cations also apply to anions. The anion, Cl-, is the same in all three salts studied here, and its density profile roughly follows its corresponding cation (as would be expected based on local electroneutrality in water). D. Temperature Dependence of ∆Gu. The free energy of unfolding of globular proteins shows a roughly parabolic dependence on temperature. The polymer used here has been shown to exhibit a similar dependence36,53 in water. We obtain the free energy of unfolding of our polymer using

( )

-∆Gu ) exp kbT

∫RR ∫RR

max

cut cut

min

exp[-W(Rg)/kbT]dRg

(3) exp[-W(Rg)/kbT]dRg

where Rmin and Rmax are the lower and higher limits of Rg. We use Rcut ) 0.75 nm to distinguish folded (Rg < Rcut) and unfolded ensembles. Changing the Rcut value over a reasonable range only affects the value of ∆Gu but not its temperature dependence. We used W(Rg) profiles from 280 to 360 K and at 1 atm to calculate ∆Gu(T) in water and in 4.9 M GdmCl solution, which is shown in Figure 7. ∆Gu(T) profiles are fit using eq 4, allowing us to extract enthalpy, entropy, and heat capacity of unfolding.

∆Gu(T) ) ∆Href u + ∆Cp(T - Tref) T(∆Sref u + ∆Cp ln(T/Tref)) (4) In water, ∆Gu is parabolic, and at 280 K, the stability of the folded states is ∼10 kJ/mol and increases to 12-13 kJ/mol near 325 K before decreasing at higher temperatures. GdmCl destabilizes folded states by ∼2 kJ/mol at room temperature and by a smaller magnitude at higher temperatures. As a result, the temperature of maximum ∆Gu (at which ∆Su ) 0) increases by ∼8-10 K. Interestingly, a similar behavior is observed in the thermodynamics of hydrophobic hydration, where the free energy of hydration is parabolic and the addition of solute-water attractions moves that profile down and shifts the maximum to higher temperatures.66 This similarity again points to the role

Figure 7. (a) Free energy of unfolding, ∆Gu(T), of the polymer in pure water and in 4.9 M GdmCl solution. Points are simulation data, and the line is a fit using eq 5. (b) Enthalpy and (c) entropy of unfolding of the polymer in pure water and in 4.9 M GdmCl solution, obtained from the fits to ∆Gu(T) data. (d) The change in ∆Hu and T∆Su between the two solutions.

of solute-solvent attractions in GdmCl-induced destabilization of folded hydrophobic polymers. Although our polymer is a simple hydrophobic homopolymer, its folding thermodynamics including the effects of GdmCl are qualitatively similar to those of globular proteins. For example, ∆Gu(T) for the protein Barstar reported by Agashe and Udgaonkar67 and on ubiquitin by Molero et al.68 show (i) parabolic temperature dependence of ∆Gu, (ii) GdmCl-induced destabilization that is larger at lower temperatures, and (iii) a corresponding shift of the temperature of maximum ∆Gu.68,69 Equation 4, which assumes the heat capacity of unfolding, ∆Cp, to be temperature independent, describes the ∆Gu(T) well. We obtain ∆Cp values in water and in GdmCl solutions to be 0.72 and 0.85 kJ/mol/K, respectively. Experiments on proteins show not only that ∆Cp increases67,69 but also that the expected increase up on addition of 5 M GdmCl is about 18-20%, similar to that observed here for the polymer.67 ∆Hu(T) and ∆Su(T) profiles in Figure 7b and c show that in water the enthalpy of unfolding is favorable, whereas the entropy change is unfavorable (negative). In GdmCl solutions, the entropy of unfolding becomes even more unfavorable but is more than compensated by a favorable enthalpy change leading to the observed destabilization of folded polymers. A favorable ∆∆Hu is also observed in calorimetric experiments on proteins unfolding in GdmCl solutions.67-69 The roughly parabolic behavior of ∆Gu(T) implies that the polymer will unfold at sufficiently cold temperatures at which ∆Gu e 0. This behavior is characteristic of hydrophobic interactions,70 which are weakened at lower temperatures, an effect that is enthalpy dominated. Addition of GdmCl to the solution lowers ∆Gu, especially at lower temperatures, shifting the “cold denaturation” temperature to the right, making it more accessible. Proteins ubiquitin68 and AS-4869 also exhibit higher cold-denaturation temperatures in GdmCl solutions. The striking similarity of the thermodynamics of unfolding of the hydrophobic polymer and of globular proteins underscores the utility of this polymer model as well as the importance of hydrophobic interactions in protein folding and in understanding GdmCl effects on protein stability. One difference in the GdmCl effects on the polymer and on proteins is noteworthy. The destabilization of folded states by

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GdmCl is prominent at temperatures below ∼360 K. Because folded states of the polymer are stable over a wider range from 230 to 450 K (as suggested by a ∆Gu(T) extrapolation), GdmCl ′ , but appears to affect only the cold unfolding temperature, Tm not the heat unfolding temperature, Tm. In contrast, many proteins are marginally stable and unfold over a temperature range of 310 to 370 K. For those proteins, GdmCl pulls the ∆Gu(T) curve down and affects both cold and heat denaturation temperatures. We note, however, that GdmCl effects on T′m and Tm are not symmetric even for typical proteins, and experiments ′ to GdmCl addition that of Tm.68 show higher sensitivity of Tm In fact, these different sensitivities are amplified for thermophilic proteins.71 Limited experimental data on GdmCl effects on thermophiles suggest a behavior similar to that observed here for the hydrophobic polymer. E. Dynamics of Hydrophobic Collapse in Salt Solutions. Addition of salts, especially at high concentrations, changes both the thermodynamic driving force for collapse as well as dynamic properties of the solvent (e.g., water diffusivity, viscosity, etc.). We calculated the water diffusivity in pure water and different salt solutions using mean square displacement data, Dwat ) 2.76, CsCl NaCl GdmCl ) 1.75, Dwat ) 1.33, and Dwat ) 1.11 in units of 10-5 Dwat cm2/s. The trend in these values is consistent with experimentally reported values of solution viscosities, which also rank in the same orderspure water < CsCl < NaCl ≈ GdmCl.72-74 How does the slowdown in water dynamics and the altered PMFs affect the dynamics of polymer collapse? We performed over 50 simulations of polymer collapse each starting from a microscopically different configuration from an ensemble of fully extended states (Rg ∼1.40 nm) in water, NaCl, CsCl, and GdmCl solutions and monitored the time evolution of Rg (Figure 8). The collapse in water and in NaCl and CsCl solutions is fast and occurs over a subnanosecond time scale, whereas in GdmCl it is about five times slower. A detailed understanding of the mechanism of hydrophobic collapse may require consideration of solvent degrees of freedom in addition to those of the polymer.50,75 Qualitatively, in NaCl and CsCl solutions, the enhanced driving force for collapse (Figure 2) and the slowdown in solvent dynamics counteract each other, leading to a folding time distribution similar to that in water (Figure 8). In contrast, in GdmCl solution, both the driving force for collapse and solvent dynamics are reduced leading to a much slower collapse. The inherent conformational dynamics of the polymer can be better quantified by calculating the diffusivity of the order parameter, D(Rg)76,77

Figure 8. (a) Time evolution of Rg averaged over 50 nonequilibrium folding simulations starting with Rg ≈ 1.40 nm in water and in 4.9 M max GdmCl, NaCl, and CsCl solutions. R*g ) (Rg - Rmin - Rmin g )/(Rg g ). Note that the y-axis is on a log scale. (b) Mean squared displacement for the translation of the center of mass of folded polymers in water and in different solutions.

(5)

Figure 9. Correlation of polymer dynamics with water diffusivity, Dsoln wat , in various solutions. Polymer dynamics are quantified by Dconf and Dtrans, the conformational and translational diffusivities, respectively. A linear fit to the Dtrans data is shown.

where τf is the average folding time. For simplicity, we assume D(Rg) to be constant, equal to Dconf, and obtain its value from eq 5. Dconf serves as a measure of conformational dynamics or diffusivity of the polymer. We also measured translational diffusivity, Dtrans, of the center of mass of folded polymers in water and in different salt solutions using mean squared displacement data shown in Figure 8b. Figure 9 shows that Dconf and Dtrans in different solutions are monotonically correlated with with water diffusivity, Dwat. Assuming the validity of Stokes-Einstein relation, D ) (kT)/ (6πηr), down to subnanometer/molecular length scales,78 we estimate Dtrans ) 4.8 × 10-6 cm2/s, for the polymer in pure water (using viscosity of SPC/E water79 η ) 0.82 cP and r )

Rgf ) 0.55 nm), which is in excellent agreement with the value from MD simulations. The Stokes-Einstein relation also suggests a simple linear relationship between polymer and water translational diffusivities, Dtrans ) (rw/Rgf)Dwat, with slope of roughly 0.25 (using the radius of a water molecule, rw ) 0.14 nm). Figure 9 shows an approximately linear relationship between Dwat and Dtrans with a slope of ∼0.22. Dconf exhibits a nonlinear relationship with the solvent dynamics, indicating the complexity of conformational dynamics involved in polymer collapse. Details of the processes involved in polymer folding and polymer translation in solution are different. Nevertheless, Dconf tracks the solvent dynamics well, and both Dconf and Dtrans are reduced by a factor of ∼5 in GdmCl solutions compared to that in bulk water.

τf ≈

∫R

Rmax min

dRg

exp[(W(Rg) - W(R'g))/kT] dR'g Rmin D(Rg)

∫

Rg

Unfolding of Hydrophobic Polymers IV. Conclusions We studied the effects of guanidinium chloride on hydrophobic interactions at molecular and larger length scales and compared them to effects of simple salts. We showed that guanidinium chloride salts out small (methane-like) hydrophobic solutes and increases the strength of their interactions in water, an effect similar to those of other salts, NaCl and CsCl. Likewise, all salts studied here increase the surface tensions of their aqueous solutions albeit to different extents. Effects of GdmCl on the collapse thermodynamics of a hydrophobic polymer are, however, different. NaCl, CsCl, and TMACl enhance the driving force for hydrophobic collapse, and GdmCl reduces it. The destabilization of folded states of a hydrophobic polymer in GdmCl solution may be puzzling in light of the strengthening of small length scale hydrophobic effects and an increase in the surface tension of GdmCl solutions. A decomposition of the free-energy of collapse into different contributions reveals that it is the attractive interactions of the multisite Gdm+ ions with the polymer that contribute to GdmCl-induced destabilization. Analysis of structure also shows a consistent picture. Whereas Na+ and Cs+ ions are depleted from the polymer vicinity, Gdm+ ions coat the polymer with their planes parallel to the polymer surface. The planarity of the Gdm+ ion may be important to its denaturing action because another multisite spherical TMA+ ion with low charge density favors folding of the hydrophobic polymer. Calculations of the free energy of polymer unfolding, ∆Gu(T), over a range of temperatures highlight the parallels between temperature dependence of thermodynamics of polymer collapse and of protein folding. In water, ∆Gu(T) shows parabolic variation with temperature that is protein-like and shows signatures of both thermal and cold-induced unfolding. In GdmCl solutions, folded states are less stable, and the colddenaturation temperature increases. Decomposition of ∆Gu shows that the GdmCl-induced destabilization is dominated by a favorable enthalpy, consistent with experimental data on proteins. Simulations show that conformational and translational dynamics of the polymer track that of solvent water in different solutions. Correspondingly, polymer collapse is fast in water, NaCl, and CsCl solutions and is considerably slowed down in GdmCl solution. Our work highlights the limitations of studies based on pairlevel interactions between small solutes to understand more complex self-assembly in aqueous solutions. Results on the thermodynamics of collapse of the hydrophobic polymer show that it better captures characteristic signatures of hydrophobicity including heat and cold denaturation and shows guanidiniuminduced destabilization that is driven by polymer-GdmCl attractive interactions. Acknowledgment. We thank the National Science Foundation for financial support of the work through NSEC DMR0642573 and BES grants. We also thank Prof. George I. Makhatadze and Prof. Angel E. Garcia for comments on this manuscript. References and Notes (1) Wetlaufer, D. B.; Coffin, R. L.; Malik, S. K.; Stoller, L. J. Am. Chem. Soc. 1964, 86, 508–514. (2) Robinson, D. R.; Jencks, W. P. J. Am. Chem. Soc. 1965, 87, 2462– 2470. (3) Nozaki, Y.; Tanford, C. J. Biol. Chem. 1963, 238, 4074–4081. (4) Alonso, D. O. V.; Dill, K. A. Biochemistry 1991, 30, 5974–5985.

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