J. Phys. Chem. B 2008, 112, 5661-5670
5661
Enthalpy-Entropy Contributions to Salt and Osmolyte Effects on Molecular-Scale Hydrophobic Hydration and Interactions Manoj V. Athawale, Sapna Sarupria, and Shekhar Garde* The Howard P. Isermann Department of Chemical & Biological Engineering, and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180 ReceiVed: May 7, 2007; In Final Form: February 7, 2008
Salts and additives can significantly affect the strength of water-mediated interactions in solution. We present results from molecular dynamics simulations focused on the thermodynamics of hydrophobic hydration, association, and the folding-unfolding of a hydrophobic polymer in water and in aqueous solutions of NaCl and of an osmolyte trimethylamine oxide (TMAO). It is known that addition of NaCl makes the hydration of hydrophobic solutes unfavorable and, correspondingly, strengthens their association at the pair as well as the many-body level (Ghosh, T.; Kalra, A.; Garde, S. J. Phys. Chem. B 2005, 109, 642), whereas the osmolyte TMAO has an almost negligible effect on the hydrophobic hydration and association (Athawale, M. V.; Dordick, J. S.; Garde, S. Biophys. J. 2005, 89, 858). Whether these effects are enthalpic or entropic in origin is not fully known. Here we perform temperature-dependent simulations to resolve the free energy into entropy and enthalpy contributions. We find that in TMAO solutions, there is an almost precise entropy-enthalpy compensation leading to the negligible effect of TMAO on hydrophobic phenomena. In contrast, in NaCl solutions, changes in enthalpy dominate, making the salt-induced strengthening of hydrophobic interactions enthalpic in origin. The resolution of total enthalpy into solute-solvent and solvent-solvent terms further shows that enthalpy changes originate primarily from solvent-solvent energy terms. Our results are consistent with experimental data on the hydration of small hydrophobic solutes by Ben-Naim and Yaacobi (Ben-Naim, A.; Yaacobi, M. J. Phys. Chem. 1974, 78, 170). In combination with recent work by Zangi, Hagen, and Berne (Zangi, R.; Hagen, M.; Berne, B. J. J. Am. Chem. Soc. 2007, 129, 4678) and the experimental data on surface tensions of salt solutions by Matubayasi et al. (Matubayasi, N.; Matsuo, H.; Yamamoto, K.; Yamaguchi, S.; Matuzawa, A. J. Colloid Interface Sci. 1999, 209, 398), our results highlight interesting length scale dependences of salt effects on hydrophobic phenomena. Although NaCl strengthens hydrophobic interactions at both small and large length scales, that effect is enthalpy-dominated at small length scales and entropydominated for large solutes and interfaces. Our results have implications for understanding of additive effects on water-mediated interactions, as well as on biocompatibility of osmolyte molecules in aqueous solutions.
I. Introduction Hydrophobic interactions are important contributors to biological and colloidal self-assembly phenomena in aqueous solutions.1-4 At the molecular level, the thermodynamics of hydrophobic effects has been quantified previously by calculating the free energy of hydration of methane-like nonpolar solutes as well as the potential of mean force between two such solutes in water.5-19 It is well-known that the unfavorable free energy of hydrophobic hydration is dominated by the negative (unfavorable) entropy of hydration.12,20-24 Correspondingly, it is the solvent entropy that favors association of molecular hydrophobic solutes in water.8,9,11,25 Biological or colloidal interactions, however, generally occur in mixed aqueous solutions that contain salt ions, cosolvents, or other additives such as osmolytes.26-37 Depending on the interactions of these additives with hydrophobic solutes and with water, and their effect on water structure, the strength of hydrophobic interactions (or other thermodynamic characteristics of hydrophobic effects) is expected to change.16,18,38-40 For example, hydrophobic interactions are strengthened in NaCl * To whom correspondence should be addressed. E-mail: gardes@ rpi.edu. Ph: 518-276-6048. Fax: 518-276-6046. Website: http:// www.rpi.edu/∼gardes.
solutions, whereas in mixed alcohol solutions, the strength of hydrophobic interactions varies non-monotonically with alcohol concentration.41,42 More recently, studies of hydrophobic effects in a solution of a potent osmolyte trimethylamine oxide (TMAO) showed that this osmolyte has a negligible effect on the strength of pair or many-body hydrophobic interactions.40 This negligible dependence of hydrophobic effects on the addition of TMAO likely explains the “compatible” nature30,43 of this osmolyte when accumulated at high concentrations in intracellular environments. To better understand the effects of additives on hydrophobic interactions, one requires not only the free-energy changes in mixed solutions but also the resolution of that free energy into entropic and enthalpic contributions. Although the effects of additives on the fundamental molecular-scale hydrophobic effects are receiving increasing attention in the literature,14,16,18,40,41,44-53 quantification of the corresponding entropy and enthalpy contributions is relatively less explored.54-56 Here we focus on the thermodynamics of hydrophobic effects in two mixed aqueous systems, NaCl solutions and TMAO solutions. We characterize hydrophobic effects by quantifying the thermodynamics of small solute hydration, their pair interactions, as well as hydrophobic effects at a many-body level
10.1021/jp073485n CCC: $40.75 © 2008 American Chemical Society Published on Web 05/01/2008
5662 J. Phys. Chem. B, Vol. 112, No. 18, 2008 by studying the folding-unfolding of a hydrophobic polymer in water, as done previously.18,40 In addition, we perform temperature-dependent simulations25 to resolve free-energy changes upon NaCl and TMAO addition into entropic and enthalpic components. In the TMAO solution, we find that the negligible effect of TMAO on hydrophobic interactions arises from an almost precise enthalpy-entropy compensation. In contrast, in NaCl solutions, we find that the strengthening of hydrophobic effects is predominantly enthalpic in origin. For NaCl solutions, we further quantify contributions from various individual solute-solvent energy terms to the total enthalpy to understand molecular origins of the observed enthalpy changes. All of our hydrophobic solutes interact with water with standard Lennard-Jones interactions which include weak attractions. There is interest in understanding the origins of salt effects on the equivalent primitive processes of cavity formation or hard-sphere (or soft-repulsive solute) dissolution in water.16,47,49-51,54-56 To this end, we report calculations on the hydration of repulsive WCA57 solutes in water and in salt solutions. These calculations underscore the sensitivity of numerical values of the absolute entropy and enthalpy of hydration on the temperature dependence of density of a given water model, which is expected from an information theory perspective58 as well as from a thorough study by Paschek.24 However, the changes in entropy and enthalpy upon salt addition are remarkably similar in calculations using simulations of a NaCl solution in SPC/E water in the NPT ensemble, or simulations in the NVT ensemble with experimental densities, and in actual experiments. Collectively, these calculations point to an enthalpic (and not entropic) origin of the salt-induced strengthening of hydrophobic effects at small length scales. Finally, our results, in combination with past experimental45 and simulation studies on the solubility of small hydrophobic solutes,59 surface tension measurements,60 and recent simulation studies on the association of nanoscale hydrophobic plates,61 point to an interesting length scale dependence of the thermodynamics of NaCl-induced strengthening of hydrophobic phenomena. Specifically, the salt-induced strengthening of hydrophobic effects is enthalpy-dominated for small solutes and entropy-dominated for large hydrophobic solutes or surfaces. II. Methods We characterized hydrophobic effects by calculating thermodynamic quantities at three different levels, as done in our previous publications.18,40 (I) To characterize hydrophobic hydration, we calculated excess chemical potentials of nonpolar solutes using test particle insertions62 in pure water and in salt and TMAO solutions of different concentrations. We studied nine different nonpolar Lennard-Jones (LJ) solutes with solutesolute ss ) 1.234 kJ/mol and the solute σss values ranging from 0.2 to 0.44 nm (in steps of 0.03 nm).40 We calculated solutesolvent or solute-additive LJ parameters using the LorentzBerthelot mixing rules.63 Configurations of pure water and aqueous NaCl (1.0, 3.2, and 4.7 mol/L) and TMAO (1, 2, and 3 mol/L) solutions were obtained from molecular dynamics (MD) simulations performed using GROMACS.64,65 TMAO, trimethylamine- oxide, (CH3)3Nd O, is represented explicitly using an all-atom description.40,66 The molecule is tetrahedral in geometry and is overall charge neutral with qO ) -0.65e, qN ) +0.44e, qC ) -0.26e, and qH ) +0.11e. Further details of the simulation methodology and force fields for TMAO are given in ref 40. Extended simple point charge model of water,67 SPC/E, was used, and the salt ions (Na+ and Cl-) were represented as spherical LJ solutes68
Athawale et al. TABLE 1: Number of Species of Each Type Included in MD Simulations Used to Characterize Hydrophobic Effects in NaCl Solutionsa
1 2 3 4 5 6 7
solute (Nsolute)
Nwater
NNa+
NCl-
salt conc., mol/L
Me(10) Me(10) Me(10) Me(10) 25-mer(1) 25-mer(1) 25-mer(1)
500 500 460 430 1000 1000 920
0 10 30 45 0 20 60
0 10 30 45 0 20 60
0.0 1.0 3.2 4.7 0.0 1.0 3.2
a Me indicates methanes, and 25-mer is the hydrophobic polymer. The last column gives the molar concentration of NaCl in the solution.
TABLE 2: Number of Species of Each Type Included in MD Simulations Used to Characterize Hydrophobic Effects in TMAO Solutionsa
1 2 3 4 5
solute (Nsolute)
Nwater
NTMAO
TMAO conc., mol/L
Me(10) Me(10) Me(10) Me(10) 25-mer(1)
550 550 550 550 2000
0 18 38 60 135
0 1 2 3 2
a Me Indicates methanes and 25-mer is the hydrophobic polymer. The last column gives the molar concentration of TMAO in the solution.
with the electronic charge placed at their center. To characterize the salt effect on equivalent primitive hydrophobic phenomena of cavity formation or hard-sphere (or repulsive soft-sphere) hydration, we performed calculations of excess chemical potentials of Weeks-Chandler-Anderson57 equivalents of LJ solutes described above in different salt solutions. (II) To characterize the thermodynamics of hydrophobic interactions, we simulated solutions of methane-like solutes in pure water and in NaCl and TMAO solutions.18,40 The methanemethane potential of mean force profile was obtained from each simulation using W(r) ) -kT ln g(r), where g(r) is the methane-methane radial distribution function.69 The number of each species used in these simulations is listed in Tables 1 and 2. We note that the number of species used in simulations for excess chemical potential calculations (hydrophobic hydration in I above) is identical, except methane molecules were not included in those simulations. (III) To quantify hydrophobic interactions at the many-body level, we studied the folding-unfolding of a hydrophobic polymersa 25-mer of methane-like monomers18,70sin water and in NaCl and TMAO solutions. The intrapolymer interactions included harmonic bond and bond-angle interactions (see more details in ref 70). The umbrella sampling technique71,72 was used to obtain the probability distribution of the radius of gyration, p(Rg), of the polymer. We calculated the PMFs along the Rg coordinate, W(Rg) ) -kT ln p(Rg), in pure water, in TMAO, and in NaCl solutions. For all three types of characterization of hydrophobic effects described above, we performed simulations at 280, 300, and 320 K, at a constant pressure of 1 bar.73 Derivatives of free energy were used to calculate the enthalpy and entropy contributions in each case at 300 K.15,25,74,75 It is known that numerical values of the enthalpy and entropy of hydrophobic hydration are sensitive to the temperature dependence of the density of the water model used.24 To investigate this aspect further, we also performed simulations
Enthalpy-Entropy Contributions to Salt
J. Phys. Chem. B, Vol. 112, No. 18, 2008 5663 TABLE 3: Experimental Values of the Enthalpy, Entropy, and Excess Chemical Potential of Methane in Pure Water and NaCl Solution45,a ∆H ∆∆H ∆S -T∆S -T∆∆S ∆µex ∆∆µex kJ/mol kJ/mol J/mol-K kJ/mol kJ/mol kJ/mol kJ/mol H2O 1 M NaCl 2 M NaCl
-10.9 -9.4 -7.0
0.0 1.5 3.9
-62.8 -62.8 -58.6
18.8 18.8 17.6
0.0 0.0 -1.2
8.4 9.2 10.0
0.0 0.8 1.6
a ∆∆ represents the thermodynamic properties associated with transfer of methane from water to a NaCl solution.
Figure 1. (a) Excess chemical potential, ∆µex, of LJ solutes as a function of solute size σss, calculated in four different TMAO solutions (0, 1, 2, and 3 mol/L) (error bars indicate one standard deviation calculated from block averages) (data taken from ref 40). (b) Enthalpy and entropy contributions to the excess chemical potential in (a) calculated for different TMAO concentrations. Arrow indicates increasing TMAO concentration. (c) Free energy, enthalpy, and entropy of water-to-TMAO-solution transfer of a methane-sized solute (σss ) 0.373 nm) as a function of TMAO concentration.
Figure 2. (a) Excess chemical potential, ∆µex, of LJ solutes as a function of solute size σss. Values calculated in four different NaCl solutions (0.0, 1.0, 3.2, and 4.7 mol/L) are shown (error bars indicate one standard deviation calculated from block averages). (b) Enthalpy and entropy contributions to the excess chemical potential in (a) calculated for different NaCl concentrations. Arrows in (a) and (b) indicate curves calculated with increasing NaCl concentration. (c) Free energy, enthalpy, and entropy of water-to-NaCl solution transfer of a methane-sized solute (σss ) 0.373 nm) as a function of NaCl concentration. (d) Comparison of water-to-NaCl-solution transfer free energy, enthalpy, and entropy obtained from simulations (lines) with experimental data from Ben-Naim45 (symbols).
of aqueous (1, 2, and 3 mol/L) NaCl solutions in the canonical (NVT) ensemble using experimental densities76 at three different temperatures (280, 300, and 320 K) and calculated the thermodynamics of hydrophobic hydration using solute insertion. III. Results and Discussion A. Enthalpy and Entropy of Hydrophobic Hydration. Figure 1a shows excess chemical potentials of hydrophobic solutes in water and in TMAO solutions. The chemical potential is large and positive, consistent with the low solubility of hydrophobic solutes in water,45 and increases with increasing solute size. This is expected because the corresponding contribution of the cavity formation process increases monotonically with solute size.74,77 Figure 2a shows similar calculations in NaCl solutions obtained from MD simulations. The differences in the hydrophobic solvation thermodynamics in TMAO and
in salt solutions are clear. Whereas addition of NaCl increases the chemical potential of hydrophobic solutes significantly (leading to salting-out),16,18 addition of TMAO decreases the chemical potential slightly, as reported previously by our group.40 For a methane-sized solute (σss ) 0.373 nm), the waterto-additive-solution transfer free energy, ∆∆µex is about +4 kJ/ mol in 3 mol/L NaCl and only about -1 kJ/mol in 3 mol/L TMAO solution. The relatively small values of water-to-TMAOsolution transfer free energies of hydrophobic solutes are consistent with experimental measurements of the thermodynamics of the transfer of hydrophobic amino acids in TMAO solutions.35 Figures 1b and 2b show the decomposition of hydrophobic hydration free energies into entropic and enthalpic contributions obtained by taking temperature derivatives of the free-energy values.24,25 In pure water, the hydration of small hydrophobic solutes is dominated by large negative entropy.20,23,24,74 For methane-sized solutes (σss ) 0.373 nm), the entropy of hydration is approximately -50 J/mol/K, in agreement with previous simulations20,24 and in qualitative agreement with experimental data. The large negative entropy of hydrophobic hydration has been interpreted in terms of solute-water translational and orientational correlations.20,21 The corresponding enthalpy of hydration is negative (favorable). The changes in the enthalpy and entropy contributions, ∆∆H and -T∆∆S, upon TMAO and salt addition are shown in Figures 1c and 2c. The ∆∆H and -T∆∆S values are near zero in a 1 mol/L TMAO solution. At higher concentrations, the enthalpy of hydration becomes unfavorable for transfer of a hydrophobic solute from water to TMAO or water to NaCl solution. In contrast, the entropy of hydration for the transfer process becomes favorable. Interestingly, for TMAO, there is an almost precise enthalpy-entropy compensation leading to the near-zero values of the free energies of hydrophobic transfer from water to TMAO solutions. In salt solutions, the unfavorable enthalpy of transfer, ∆∆H, makes the dominant contribution to the free-energy change, ∆∆µex, thus making the salting-out phenomenon of small solutes primarily enthalpic in origin. The relative changes (∆∆) in free energy, enthalpy, and entropy obtained here in NaCl solutions are consistent with the experimental values reported by Ben-Naim (shown by symbols in Figure 2d).45 The experimental values of ∆µex, ∆H, and ∆S for the transfer of a methane from vacuum to NaCl solution reported by Ben-Naim45 are given in Table 3. For comparison, corresponding values calculated from MD simulations in NPT and NVT ensembles are shown in Table 4. The experimental data are available only up to a 2 mol/L concentration of NaCl, and although the absolute values of ∆µex, ∆H, and ∆S calculated here agree only qualitatively with the reported experimental values, the changes (i.e., ∆∆) relative to that in pure water are in excellent agreement with the experimental data. Our calculations of the thermodynamics of the hydration of methane in pure water (∆µex ) 9.4 kJ/mol) and in a 1 mol/L NaCl solution (∆µex ) 10.5 kJ/mol) are also consistent with those from a
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TABLE 4: (A) Enthalpy, Entropy, and Excess Chemical Potential of Transfer of a Methane-Sized Particle from Vacuum to a NaCl Solution Obtained from MD Simulations in the NPT Ensemble; (B) Enthalpy, Entropy, and Excess Chemical Potential of Transfer of Hydrophobic Solute (σss ) 0.32 nm) from Vacuum to a NaCl Solution Calculated from MD Simulations in the NVT Ensemble Performed Using the Experimental Solution Densitya ensemble
solvent
∆H kJ/mol
∆∆H kJ/mol
∆S J/mol-K
-T∆S kJ/mol
-T∆∆S kJ/mol
∆µex kJ/mol
∆∆µex kJ/mol
NPT NPT NPT
H2O 1 M NaCl 2 M NaCl
-5.5 -3.6 -1.4
0.0 1.9 4.1
(A) -49.7 -46.9 -43.5
14.9 14.1 13.1
0.0 -0.8 -1.8
9.4 10.5 11.7
0.0 1.1 2.3
NVT NVT NVT
H2O 1 M NaCl 2 M NaCl
-9.6 -7.4 -6.8
0.0 2.2 2.8
(B) -55.9 -51.5 -53.2
16.8 15.4 16.0
0.0 -1.4 -0.8
7.2 8.1 9.1
0.0 0.9 1.9
a
∆∆ represents the thermodynamic properties associated with water-to-NaCl-solution transfer of the hydrophobic solute.
previous simulation study by Paul Smith,14 who reported ∆µex ) 9.4 kJ/mol in water and 10.7 kJ/mol in 1.0 mol/L NaCl. Smith reported ∆∆H ) +3 kJ/mol in 1 mol/L NaCl, whereas our values of the enthalpy change ∆∆H are comparable but somewhat smaller, equal to 1.9 (for NPT) and 2.2 kJ/mol (for NVT runs and for a slightly smaller solute). The enthalpy and entropy reported above are referred to in standard thermodynamic literature as “solvation enthalpy” and “solvation entropy”. That is, ∆H ) -T2[∂(∆G/T)/∂T]P and ∆S ) -[∂∆G/∂T]P, as typically measured in experiments.44,45 Naturally, if the change in free energy upon salt addition, ∆∆G, is dominated by ∆∆H, we refer the salt effect to be “enthalpic” in nature. We believe such assignment to be unequivocal and experimentally verifiable. Alternative views exist on this issue. For example, motivated by the development by Yu and Karplus78 and later by Guillot and Guissani10 and Lee,79 the hydration free energy can be written as
∆G ) (∆Usw + ∆Uww) - T(∆Ssw + ∆Uww/T)
(1)
where ∆Usw, ∆Uww, and ∆Ssw are changes in the so-called “solute-water” energy, water-water energy, and “solutewater” entropy, respectively, and the minor pressure-volume term is reasonably neglected. For dissolution of a hard-sphere (or equivalent WCA solute), ∆Usw is exactly (or very nearly) zero, and ∆G numerically equals -T∆Ssw. On the basis of this numerical equivalence, one might argue55,56,80 that salt effects or, for that matter, any other effect would be purely entropic in origin for hard-sphere dissolution. Our results based on the “solvation entropy” perspective might appear to be in contrast with those based on “solutesolvent entropy”.55 We note, however, that as far as we are aware, the so-called solute-solvent entropy is formally not a temperature derivative of free energy but simply equal to -∆GHS/T (where HS refers to a hard-sphere solute). Naturally, changes in ∆GHS at a given temperature will be numerically equal to -T∆GHS/T (or -T∆Ssw) and therefore dominated by solute-solvent entropy. However, we stick to solvation enthalpy and entropy in the rest of this paper and characterize the thermodynamics to be enthalpy-dominated if indeed solvation enthalpy dominates the process. We note that numerical values of solvation entropy and enthalpy are sensitive to the temperature dependence of the density of the water model used. This aspect has been thoroughly analyzed and discussed by Paschek.24 For hard-sphere solutes, the information theory perspective58 suggests that the enthalpy of hydration is approximately zero at the temperature of maximum density (TMD) and becomes positive (unfavorable) at higher temperatures. Thus, depending on the water model (and specifically its TMD), the entropy and enthalpy of hard-
sphere hydration at temperatures greater than TMD may be comparable in magnitude, with enthalpy dominating the hydration at “sufficiently high” temperatures. Here, simulations of SPC/E water in the NPT ensemble give the entropy of hydration of a methane-sized LJ solute to be ∼-50 J/mol/K, compared to the experimental value of -62.8 J/mol/K for methane,45 consistent with a different temperature dependence of the density in SPC/E and real water systems. The addition of salts or osmolytes to water changes the density as well as its temperature dependence quantitatively. It appears that those changes are reproduced well by the SPC/E model, as shown by the good agreement between ∆∆S and ∆∆H values calculated here and those in experiments.45 Further calculations of ∆∆S and ∆∆H for the hydration of LJ as well as WCA solutes in the NVT ensemble using experimental densities of aqueous salt solutions at three different temperatures (280, 300, and 320 K)76 (Figures 3 and 4) give similar results. To summarize, the ∆∆H and ∆∆S values upon salt addition are similar if not numerically identical (for LJ and WCA solutes whether estimated using isobaric simulations or using experimental densities), indicating that our conclusion of the solvationenthalpy-dominated nature of salt effects is reasonable. B. Comparing Hydrophobic Hydration in TMAO and That in Other Osmolyte Solutions. Our calculations above show that the negligible effect of the well-known “compatible” osmolyte TMAO on hydrophobic hydration arises from an approximate enthalpy-entropy compensation. Experimental data on the transfer thermodynamics of hydrophobic solutes from water to other osmolytes (e.g., the well-known “perturbing” osmolyte urea or the denaturant guanidinium hydrochloride (GuHCl)) are also available. Do the thermodynamics of hydrophobic hydration display similar characteristics in solutions of these osmolytes? Graziano54 has analyzed the experimental data from Wetlaufer et al.81 to obtain the thermodynamics of transfer of various hydrophobic solutes from water to urea and to GuHCl solutions. For the transfer of a methane molecule from water to urea or GuHCl solutions, Graziano reports ∆∆µex ) +0.8 kJ/mol, ∆∆H ) +5.4 kJ/mol, ∆∆S ) +15.3 J/mol/K for water to 7 mol/L urea; and for water to 4.9 mol/L GuHCl, ∆∆µex ) +1.0 kJ/ mol, ∆∆H ) +6.2 kJ/mol, and ∆∆S ) +17.5 J/mol/K. Our calculations for the transfer of a methane molecule from water to 3 mol/L TMAO solution yield ∆∆µex ) -0.8 kJ/mol, ∆∆H ) +3.5 kJ/mol, and ∆∆S ) +14.2 J/mol/K. Interestingly, ∆µex values are rather small in all three cases (i.e., for urea and GuHCl obtained from experiments and for TMAO obtained here); transfer of methane to urea and GuHCl solutions is slightly unfavorable, whereas transfer to a TMAO solution is slightly favorable. Further, the enthalpy of transfer is unfavorable in all
Enthalpy-Entropy Contributions to Salt
Figure 3. (a) Excess chemical potential, ∆µex, of LJ solutes as a function of solute size σss, obtained from simulations using experimental values for solution density. Results for hydration in four different NaCl solutions (0.0, 1.0, 2.0, and 3.0 mol/L) are shown (error bars indicate one standard deviation calculated from block averages). (b) Enthalpy and entropy contributions to the excess chemical potential in (a) calculated for different NaCl concentrations. Arrows in (a) and (b) indicate curves calculated with increasing NaCl concentration. (c) Free energy, enthalpy, and entropy of water-to-NaCl-solution transfer of a solute with σss ) 0.32 nm as a function of NaCl concentration. (d) Comparison of water-to-NaCl-solution transfer free energy, enthalpy, and entropy obtained from simulations (lines) with experimental data from Ben-Naim45 (symbols).
Figure 4. (a) Excess chemical potential, ∆µex, of WCA solutes as a function of solute size σss, obtained from simulations using experimental values for solution density. Results for hydration in four different NaCl solutions (0.0, 1.0, 2.0, and 3.0 mol/L) are shown (error bars indicate one standard deviation calculated from block averages). (b) Enthalpy and entropy contributions to the excess chemical potential in (a) calculated for different NaCl concentrations. Arrows in (a) and (b) indicate increasing NaCl concentration. (c) Free energy, enthalpy, and entropy of water-to-NaCl-solution transfer of a solute with σss ) 0.32 nm, as a function of NaCl concentration. (d) Comparison of water-toNaCl-solution transfer free energy, enthalpy, and entropy obtained from simulations (lines) with experimental data (points) from Ben-Naim.45
cases, and the entropy of transfer is similar in magnitude and favorable and is about 25% of the magnitude of the hydration entropy of methane in water. These similarities between the two osmolytes TMAO and urea and the denaturant GuHCl in terms of their effects on hydrophobic hydration are indeed noteworthy. Urea, classified as a “perturbing osmolyte”, is accumulated in the intracellular compartments of certain organisms along with TMAO to help counteract osmotic stress in a controlled manner.27 Small changes in the relative concentration of urea and TMAO can provide a finer control of protein stability.
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Figure 5. (a) Methane-methane potentials of mean force, W(r) ) -kT ln g(r), in pure water and in aqueous TMAO solutions of concentrations of 1, 2, and 3 M (data taken from ref 40). (b) Enthalpy and entropy contributions to the methane-methane potentials of mean force. Inset: W(r), ∆H(r), and -T∆S(r) at the contact minimum, r ) 0.39 nm, as a function of TMAO concentration.
Specifically, in a 1:2 TMAO/urea mixture, TMAO almost perfectly counteracts the perturbing effect of urea.82 Interestingly, the free energies of methane transfer from water to 3 mol/L TMAO and to 7 mol/L urea solutions (approximately 1:2 solution) reported above are equal in magnitude and opposite in sign, and they cancel each other. Whether these observations are fortuitous or directly relevant to biological counteraction observed in 1:2 TMAO/urea mixtures27,30,43 is not entirely clear. Finally, we note that enthalpy-entropy compensation in highconcentration (6.9 mol/L) urea solutions has been reported in independent studies by the van Gunsteren group,50,51 although other studies46,48,83 report strengthening/weakening of hydrophobic interactions in aqueous solutions of urea. C. Enthalpy and entropy of Hydrophobic Interactions at the Pair and Many-Body Level. Figure 5a shows the free energy of interaction (i.e., PMF) between methanes in water and in 1, 2, and 3 mol/L aqueous TMAO solutions obtained from MD simulations.40 Similarly, Figure 6a shows PMFs between methane molecules in pure water and in NaCl solutions of different concentrations. The PMF profiles in Figure 5a indicate that TMAO has a negligible effect on the relative thermodynamic stability of contact (r ) 0.39 nm) and solventseparated (r ) 0.72 nm) conformations compared to that in pure water, as observed previously.40 In contrast, we find that the addition of NaCl significantly stabilizes the contact configurations, as indicated by the decreasing free energy of contact formation with increasing salt concentration, in agreement with results of Ghosh et al.18 obtained using a different water model. TMAO and NaCl affect the desolvation barrier at r ) 0.57 nm differently and, consequently, will have a different effect on the contact formation kinetics. To resolve the PMF into solvation enthalpy and entropy contributions, we calculated PMF profiles at three different temperatures in solutions of increasing TMAO and NaCl concentrations. The enthalpy and entropy of hydrophobic interactions in TMAO and NaCl solutions obtained by taking
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Figure 7. (a) Conformational free energy, W(Rg) ) -kT ln p(Rg), of a hydrophobic polymer (25-mer) in pure water and in a 2 M TMAO solution (data taken from ref 40). (b) Enthalpy and entropy contributions to the folding/unfolding free energy of the hydrophobic polymer in (a).
Figure 6. (a) Methane-methane potentials of mean force, W(r) ) -kT ln g(r), in pure water and in aqueous NaCl solutions of concentrations of 1.0, 3.2, and 4.7 M. (b) Enthalpy and entropy contributions to the potentials of mean force. Inset: W(r), ∆H(r), and -T∆S(r) at the contact minimum, r ) 0.39 nm, as a function of NaCl concentration.
the temperature derivative are plotted in Figures 5b and 6b, respectively. Consistent with previous studies,8,9,22,25 association of hydrophobic solutes (characterized by the contact minimum near 0.39 nm) is favored by the entropic contribution. That entropic driving force is attributed to the gain in entropy by translationally and orientationally restricted water molecules near hydrophobic solutes that are released into the bulk upon the association of solutes. In contrast, the enthalpy of hydrophobic association is unfavorable. The solvent-separated minimum configuration at a methane-methane separation of 0.72 nm is stabilized by enthalpy, and the corresponding entropy is unfavorable.25 Addition of TMAO to water changes both enthalpic and entropic contributions. As would be expected from single-solute hydration thermodynamics in TMAO solution, the entropic driving force for hydrophobic association decreases upon TMAO addition. Simultaneously, the enthalpy of association becomes less unfavorable. Interestingly, again, there appears to be a precise enthalpy-entropy compensation leading effectively to a negligible change in the free energy of the interactions of methanes in water upon addition of TMAO up to a concentration of 3 mol/L. The inset of Figure 5b shows this enthalpy-entropy compensation for the contact-minimum configuration of methanes clearly. Similarly, as expected from the hydration of small solutes in aqueous solutions of NaCl, the entropic driving force for hydrophobic association decreases, whereas the enthalpy of association becomes increasingly favorable (see Figure 6b). However, in contrast to TMAO, the net effect is the stabilization of methane-methane contact configurations, arising from the decrease in the unfavorable enthalpy of association. Thus, consistent with our calculation of the thermodynamics of hydrophobic hydration, enhanced hydrophobic association in NaCl solutions is primarily enthalpic in nature. The methane-methane pair PMFs, although qualitatively relevant to the macroscopic assembly, do not capture the many-
Figure 8. (a) Conformational free energy of the hydrophobic polymer in pure water and NaCl solutions of concentrations 1.0 and 3.2 M. (b) Enthalpy (solid lines) and entropy (dashed lines) contributions to the free energy of folding/unfolding of the polymer in (a).
body aspect of hydrophobic interactions.18,70,84 Systematic extensions to calculate three-, four-, and higher body interactions have been attempted85-87 but are complicated by the dimensionality of the problem. Instead, we have recently investigated the folding-unfolding of a hydrophobic polymer in water and in additive solutions that includes many-body hydrophobic interactions18,70 in the context of macromolecular folding. Figure 7a shows the conformational free-energy profile of a hydrophobic polymer along the Rg coordinate in pure water and in 2 mol/L TMAO solution.40 The intrapolymer energy (bondangle) and the polymer-water energy terms make the unfolded state of this polymer favorable in water. Interestingly, the addition of TMAO has a negligible effect on the folding/ unfolding equilibrium of the polymer, whereas addition of salt stabilizes the folded states of the polymer (see Figure 8a) significantly. Figure 7b shows the corresponding enthalpy and entropy contributions obtained by taking the temperature derivative of the PMFs in TMAO solutions at three different temperatures. It is clear that the collapse of the hydrophobic polymer is favored by entropy, whereas the enthalpy of folding
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is unfavorable. The entropy-driven nature of the collapse indicates that although folding of this attractive C-25mer polymer includes many-body effects, its overall thermodynamics are similar to those of small solutes with an effective length scale below the crossover length scale. This is not surprising as attractive interactions reduce the effective length scale of a solute. The enthalpy and entropy of folding are sensitive to the concentration of TMAO, and we find that addition of 2 mol/L TMAO alters both contributions; the entropy of folding becomes less favorable compared to that in pure water, whereas the enthalpy of folding becomes less unfavorable. We find that changes in the enthalpy and entropy cancel each other, leading to a negligible change in the observed free energy of polymer folding in TMAO solutions. Figure 8b shows the enthalpy and entropy contributions to the polymer PMF in aqueous solutions of NaCl. In pure water, the folding of the polymer from extended to compact folded states is driven primarily by entropy, whereas the enthalpy of folding is unfavorable. Upon addition of NaCl, the entropic driving force decreases somewhat, but the enthalpy contribution becomes relatively favorable. As a result, compact states are increasingly stabilized in NaCl solution, with the additional thermodynamic stability dominated by the enthalpic component. This observation is consistent with data for small solute hydration and interactions in NaCl solutions as presented above. D. Factors Contributing to Enthalpy Changes in NaCl Solutions. At 1 atm, the pressure-volume terms are negligible, and the changes in the hydrophobic hydration or association enthalpy upon addition of salt primarily originate from constituent energetic terms. We calculated average solute-solvent and solvent-solvent interactions in different salt solutions to further understand the origin of enthalpy changes. Here, solute-solvent terms include either interactions of a single methane with water and salt (denoted by ∆UMe-solvt in the case of hydration) or the interactions of a pair of methanes held fixed at a given distance r with water, the other eight methanes, and salt ions (denoted by ∆UMe-Me-solvt(r) in the case of hydrophobic interactions). We then define the “solvent-solvent” term simply by subtracting the solute-solvent contribution from the total enthalpy change as follows. For hydrophobic hydration
∆Hsolvt ) ∆H - ∆UMe-solvt
(2)
and for hydrophobic interactions
∆Hsolvt(r) ) ∆H(r) - ∆UMe-Me-solvt(r) - UMe-Me(r) (3) A similar separation has been employed successfully in a prior study to understand the pressure effects on hydrophobic interactions.25 Configurations obtained from MD simulations were used to calculate the energetic contributions in the equations above. Figure 9a shows different energetic contributions to the enthalpy of hydration of a methane molecule in water and in NaCl solutions (1.0, 3.2, and 4.7 mol/L). Interactions of methane with sodium and chloride ions are relatively small in magnitude, make favorable contributions to the enthalpy of hydration, and increase linearly in magnitude with increasing salt concentration. This trend can be understood from the methane-Na+ and methane-Cl- pair density distribution functions shown in Figure 9c and d. The local (as well as bulk) density of salt ions increases, leading to more favorable methane-salt ion interactions with increasing salt concentration. Interestingly, the wellhydrated (smaller) Na+ ion is somewhat excluded from the region in close proximity of methane, whereas the density of
Figure 9. (a) Interaction energy contributions to the enthalpy of hydration of methane in aqueous NaCl solutions, as a function of NaCl concentration (1.0, 3.2, and 4.7 M). The values are referenced to those in pure water. Points are simulation data, and dashed lines guide the eye. The solid line is the total enthalpy of hydration, the same as that in Figure 2c. (b) Density distribution functions of methane with water oxygen, Fbulk / gMe-water(r) (c) with Na+ ions, Fbulk / gMe-Na+(r), and (d) with Cl- ions, Fbulk * gMe-Cl-(r).
the Cl- ions is comparatively higher near methane, as observed previously.16,18 These subtle differences in the local densities also explain the slightly higher magnitude of the methane-Clcontribution to the enthalpy compared to methane-Na+ contribution shown in Figure 9a. The preferential exclusion of salt ions from the vicinity of a hydrophobic solute is expected to lead to preferential hydration of that solute. The methane-water radial distribution functions in salt solutions studied previously indeed show such a behavior.18,55 However, when we consider the absolute number density of water molecules, Fbulk / gMe-water(r), we find that there is a slight depletion of water density in the vicinity of methane (see Figure 9b). As a result, with the addition of salt, the methane-water interactions decrease in magnitude, compared to that in pure water, making a positive (unfavorable) contribution to the ∆∆H. Interestingly, the gain in the interaction energy of methane with salt ions almost exactly compensates for the loss of its interaction with water, leading to ∆∆H ≈ ∆∆Hsolvt (see Figure 9a). In other words, the change in the enthalpy of hydration of a hydrophobic solute upon the addition of salt, ∆∆H, is dominated by the changes in the solvent-solvent interactions that include water-water, water-salt, and salt-salt interactions. Because the absolute magnitude of solvent-solvent interactions and their relative fluctuations are large and changes in those interactions are rather small and contribute to the hydration enthalpy, it is presently difficult to further resolve the solventsolvent interactions to pinpoint whether water-water, watersalt, or salt-salt interactions dominate the overall enthalpy change. Calculations of methane-pair-solvent interactions (see Figure 10) performed to understand the salt effects on hydrophobic interactions are consistent with the hydration data. Specifically, as two methanes associate in solution, the methane-salt interactions become unfavorable, as might be expected from the above trends in methane hydration data. Correspond-
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Figure 10. Solvent contribution to the enthalpy of association of two methanes in water and in aqueous NaCl solutions of different concentrations (1.0, 3.2, and 4.7 M). Points in the main panel show the total enthalpy of association at 4.7 M concentration (same as that in Figure 6b.) and should be compared to the dotted line indicating ∆Hsolvt in a 4.7 M NaCl solution. Inset: the contribution of Me-Me solvent energy to the total enthalpy.
ingly, methane-water interactions become favorable by approximately the same magnitude. Thus, the methane-methanesolvent energetic interactions are relatively insensitive to salt concentration (as shown in the inset of Figure 10). Similar to the observation made for hydration, we find that ∆∆H(r) ≈ ∆∆Hsolvt(r), indicating that solvent-solvent interactions again dominate the overall enthalpy changes upon salt addition. E. Length Scale Dependence of the Enthalpic Versus Entropic Nature of Salt Effects. Our results on the hydration of molecular hydrophobic solutes and their association indicate that addition of salt strengthens hydrophobic interactions, whereas addition of TMAO affects hydrophobic interactions negligibly. Interestingly, the effects of NaCl and TMAO addition on the vapor-liquid interfacial tension of a water solution also show a similar behavior; NaCl increases the surface tension,60 whereas TMAO has a comparatively negligible effect on the surface tension of its aqueous solution.88 This similarity however hides an important difference in the hydration thermodynamics of small and large solutes, as described below. In their experimental study, Matubayasi et al.60 obtained thermodynamic quantities including the free energy, entropy, and enthalpy of vapor-liquid interface formation in pure water and in aqueous NaCl solutions. As expected, in pure water, they found that the entropy of surface formation is positive (favorable), whereas the enthalpy of surface formation is positive (unfavorable). Interestingly, with the addition of NaCl, the relative entropy change is negative (unfavorable) and dominates the free energy, whereas the relative enthalpy change is somewhat favorable. We note however that the magnitudes of these changes in entropy, enthalpy, and free energy of surface formation are small. Similar observations were made recently by Zangi et al.61 in their simulation study on the effect of ions on hydrophobic interactions between nanoscale plates. Their thermodynamic analysis shows that ions of high charge density (i.e., ions similar to Na+ and Cl-) have a salting-out effect that is dominantly entropic in origin. Both of these results on the entropy and enthalpy contributions are in contrast to our results on the hydration and association of methanes as well as the folding-unfolding of a hydrophobic 25-mer in NaCl solutions. On the other hand, our results are in excellent agreement with the experimental data on the solubility of methane in
Athawale et al. NaCl solutions,45 which also indicate that the increase in the solvation free energy of small solutes in NaCl solutions is enthalpic in origin and the contribution due to the change in entropy is rather small. In a complementary simulation study, Mancera59 showed that there is an enthalpic penalty for hydration of a methane in NaCl solution as compared to that in pure water and that the unfavorable enthalpy originates from an increased number of broken water-water hydrogen bonds in NaCl solution (especially in the hydration shell of methane). This conclusion is consistent with our results that indicate that the hydration of small solutes in NaCl solution is enthalpic in origin, with the dominant contribution originating from unfavorable solvent-solvent interactions. What is the origin of these different thermodynamic characteristics and contrasting results obtained from different studies? Several recent publications have underscored the importance of length-scale-dependent hydrophobic phenomena.4,70,74,89 The thermodynamic as well as structural aspects of the hydration of hydrophobic solutes changes gradually as the solute size is increased from small to large. Specifically, small solutes can be accommodated in the open hydrogen-bonded structure of liquid water by molecular-scale thermal fluctuations, whereas the hydration of larger solutes requires the formation of an interface similar to the vapor-liquid interface of water. Correspondingly, the hydration of a molecular hydrophobic solute is dominated by large negative entropy, whereas the entropy of interface formation is small but favorable, and the hydration of large solutes is governed by unfavorable enthalpy. Interestingly, for salt effects on hydrophobic hydration and association, a similar length scale dependence is at play, albeit in the opposite manner. The work of Matubayasi et al.60 and Zangi et al.61 shows that for large length scale hydration, salt-induced hydrophobicity and salting-out is entropic in nature (i.e., dominated by unfavorable entropy), whereas at the molecular length scales, salt effects are enthalpic in nature (i.e., dominated by unfavorable enthalpy). Correspondingly, the mechanisms of salting-out at small and large length scales are different; Mancera indicates that the addition of salt makes the enthalpy unfavorable by breaking the water-water hydrogen bonds in the hydration shells of methane, whereas for large solutes, Zangi et al.61 show that it is the salt exclusion in the vicinity of hydrophobic solutes that reduces configurational entropy. To our knowledge, this is the first time that the length scale dependence of the thermodynamics of salt-effects has been highlighted, although the disparity between molecular-scale and nanoscale hydration in salt solution was also noted by Zangi et al. recently.61 IV. Conclusions To understand the effects of additives on fundamental hydrophobic phenomena, we focused on the thermodynamics of hydrophobic hydration and interactions in solutions of NaCl and of osmolyte trimethylamine oxide (TMAO) in water. We quantified the molecular-scale hydrophobic effect by studying three different processes, hydration of a methane, association of two methanes, and the folding-unfolding of a hydrophobic polymer in aqueous solutions. We find that the addition of NaCl strengthens the hydrophobic interactions,18 whereas addition of TMAO to an aqueous solution has a negligible effect on hydrophobic interactions.40 Resolution of the free energy into hydration enthalpy and entropy contributions provides further insights. In TMAO solutions, we find that for all manifestations
Enthalpy-Entropy Contributions to Salt of hydrophobic effectsshydration, association, and foldings there is an almost precise enthalpy-entropy compensation leading to the negligible effect of TMAO on hydrophobic effects. The direction of changes in the entropy and enthalpy upon the addition of TMAO is consistent in hydration, association, and folding. Specifically, the entropic driving force is weakened relative to that in bulk water, whereas the enthalpic contribution for association or folding becomes less unfavorable. In NaCl solutions, although the changes in the entropy and enthalpy of hydrophobic phenomena are in a similar direction as that in TMAO, the enthalpy contribution is larger in magnitude and dominates, leading to lowering of the solubility of non-polar solutes or strengthening of hydrophobic interactions in NaCl solutions. In other words, the salt-induced strengthening of hydrophobic interactions for small solutes is enthalpic in origin. Calculations of different energetic terms in NaCl solutions reveal that the unfavorable changes in the enthalpy of hydrophobic hydration upon addition of NaCl originate from solvent-solvent interactions and not from solute-solvent interactions. This observation and complementary calculations of the thermodynamics of WCA solutes indicate that a similar conclusion will hold for the hydration of purely repulsive solutes in NaCl solutions, further implying that the observed reduction in the probability of cavity formation in NaCl solutions15 is primarily enthalpic in origin. Our results also highlight another important aspect of the additive effects on hydrophobic phenomena, namely, their dependence on solute length scale. Specifically, our results, previous simulations,59 as well as experimental solubility data on small solutes45 indicate the salting-out of hydrophobic solutes or the salt-induced strengthening of hydrophobic interactions to be enthalpic in nature at small length scales. At larger length scales, the hydration is governed by the process of interface formation, and corresponding salt effects are entropic in nature, as indicated by the temperature-dependent surface tensions of aqueous solutions60 and by simulations of the association of nanoscopic plates in the presence of ions.61 Acknowledgment. S.G. acknowledges partial financial support of the ACS-PRF AC grant and NSF-NSEC and NSF-BES grants. S.G. also acknowledges Prof. Ravi Kane and Prof. Henry Ashbaugh for insightful discussions on this topic. We thank one of the reviewers for extensive detailed comments on the manuscript. References and Notes (1) Kauzmann, W. AdV. Protein Chem. 1959, 14, 1. (2) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; John Wiley: New York, 1973. (3) Dill, K. A. Biochemistry 1990, 29, 7133. (4) Chandler, D. Nature 2005, 437, 640. (5) Pratt, L. R.; Chandler, D. J. Chem. Phys. 1977, 67, 3683. (6) Pangali, C.; Rao, M.; Berne, B. J. J. Chem. Phys. 1979, 71, 2975. (7) Pratt, L. R.; Chandler, D. J. Chem. Phys. 1980, 73, 3434. (8) Smith, D. E.; Zhang, L.; Haymet, A. D. J. J. Am. Chem. Soc. 1992, 114, 5875. (9) Smith, D. E.; Haymet, A. D. J. J. Chem. Phys. 1993, 98, 6445. (10) Guillot, Y.; Guissani, B. J. Chem. Phys. 1993, 99, 8075. (11) Ludemann, S.; Schreiber, H.; Absher, R.; Steinhauser, O. J. Chem. Phys. 1996, 104, 286. (12) Hummer, G.; Garde, S.; Garcia, A. E.; Pohorille, A.; Pratt, L. R. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 8951. (13) Mountain, R. D.; Thirumalai, D. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 8436. (14) Smith, P. E. J. Phys. Chem. B 1999, 103, 525. (15) Hummer, G.; Garde, S.; Garcia, A. E.; Pratt, L. R. Chem. Phys. 2000, 256, 349. (16) Kalra, A.; Tugcu, N.; Cramer, S. M.; Garde, S. J. Phys. Chem. B 2001, 105, 6380.
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