Langmuir 2007, 23, 12795-12798
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Enhancing the Hydrophobic Effect in Confined Water Nanodrops Palla Venkata Gopala Rao, K. S. Gandhi, and K. G. Ayappa* Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India ReceiVed July 28, 2007. In Final Form: October 25, 2007 The distribution of hydrophobic solutes, such as methane, enclosed in a nanosized water droplet contained in a reverse micelle of diameter 2.82 nm is investigated using Monte Carlo simulations. The effect of the hydrophobic solute’s atomic diameter on the solute-solute potential of mean force is also studied. The study reveals that confinement has a strong influence on the solute’s tendency to associate. The potential of mean force exhibits only a single minimum, indicating that the contact pair is the only stable configuration between solutes. The solvent-separated pair that is universally observed for small solutes in bulk water is conspicuously absent. This enhanced hydrophobic effect is attributed to the lack of sufficient water to completely hydrate and stabilize the solvent-separated configurations. The study is expected to be important in understanding the role of hydrophobic forces during protein folding and nucleation under confinement.
1. Introduction The interactions between hydrophobic entities mediated by water have been investigated widely over many decades, and several reviews,1-3 cover this vast subject and its implications for self-assembly and protein folding. Early theoretical4 and simulation studies,5 coupled with more recent and extensive molecular simulations, have shed light on the subtle interplay between enthalpic, entropic, and size effects when a hydrophobic entity is surrounded by water.6-12 These studies aim to provide a molecular interpretation of the well-accepted signatures of the hydrophobic effect illustrated by weakly soluble apolar solutes, namely, the positive solvation free-energy change, negative entropy of solvation change, positive heat capacity, and solubility minimum with temperature. A measure of the strength of the interaction between a solute pair in water is obtained from the potential of mean force (PMF). The PMF represents the mean force between a pair of solute particles after averaging over all possible solvent configurations. When two apolar solutes such as methane are immersed in water, the PMF reveals two minima. The first minimum indicates the stability of the contact solute pair, and the second, weaker minimum indicates the presence of a solvent-separated pair. Although the thermodynamics of the hydrophobic effect has been investigated widely for solutes in bulk water, the influence of confinement on hydrophobic interaction has received little attention. Recent simulations of solutes in water confined in nanometer (1-4 nm)-sized hydrophobic cavities13 reveal that apolar solutes such as methane prefer to reside at the surface of the cavity and the solvent-separated minimum observed in bulk water is not observed. In this * Corresponding author. E-mail:
[email protected]. Tel: 011-91-80-22932769 (3600085). (1) Pratt, L. R. Annu. ReV. Phys. Chem. 2002, 53, 409-436. (2) Widom, B.; Bhimalapuram, P.; Koga, K. Phys. Chem. Chem. Phys. 2003, 5, 3085-3093. (3) Chandler, D. Nature 2005, 437, 640-647. (4) Pratt, L. R.; Chandler, D. J. Chem. Phys. 1977, 67, 3683-3704. (5) Pangali, C.; Rao, M.; Berne, B. J. J. Chem. Phys. 1979, 71, 2975-2981. (6) Guillot, B.; Guissani, Y. J. Chem. Phys. 1993, 99, 8075-8094. (7) Shimizu, S.; Chan, H. S. J. Chem. Phys. 2000, 113, 4683-4700. (8) Koga, K. J. Chem. Phys. 2004, 121, 7304-7312. (9) Paschek, D. J. Chem. Phys. 2004, 120, 6674-6690. (10) Raschke, T. M.; Levitt, M. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 67776782. (11) Lu¨demann, S.; Schreiber, H.; Abseher, R.; Steinhauser, O. J. Chem. Phys. 1996, 104, 286-295. (12) Rajamani, S.; Truskett, T. M.; Garde, S. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 9475-9480. (13) Vaitheeswaran, S.; Thirumalai, D. J. Am. Chem. Soc. 2006, 128, 1349013496.
communication, we study the interaction between small apolar solutes immersed in water confined within a reverse micelle of radius 14.1 Å. Reverse micelles are formed in oil-water-surfactant mixtures where oil forms the continuous phase, with polar surfactant head groups forming a hydrophilic cavity encasing water. The radius of the reverse micelle depends on the molar ratio of water to surfactant. The model for the sodium bis(2-ethylhexyl) sulfosuccinate or Na-AOT reverse micelle used in this study is similar to that used in earlier simulation studies where the structure and dynamics of water as a function of the reverse micelle size and counterions in the reverse micelle14,15 as well as the hydration and exchange of ions have been investigated.16 Confinement or “crowding” is increasingly known to play an important role in protein folding and is significant while elucidating folding pathways in environments that resemble the geometric and functional characteristics of living cells.17 In this regard, studies on the folding and unfolding of proteins encapsulated in reverse micelles18-20 have been carried out. The confined environment in reverse micelles can force fold proteins that are unfolded in free solution21 and cause the refolding of protein aggregates.22 In this communication, we show that when small hydrophobic solutes such as methane are confined in a reverse micelle only a single contact minimum is found in the PMF. The secondary minimum in the PMF that corresponds to the solvent-separated solute is conspicuously absent. This suggests that confinement induces a tendency for the hydrophobic particles to associate, and aggregation is observed to occur within the aqueous core of the reverse micelle. A study conducted by varying the van der Waals radii of the solute particles with fixed interparticle interactions reveals that the formation of a stable contact pair or the tendency to aggregate increases with particle size. (14) Faeder, J.; Ladanyi, B. M. J. Phys. Chem. B 2000, 104, 1033-1046. (15) Harpham, M.; Ladanyi, B.; Levinger, N. J. Phys. Chem. B 2005, 109, 16891-16900. (16) Pal, S.; Vishal, G.; Gandhi, K. S.; Ayappa, K. G. Langmuir 2005, 21, 767-778. (17) Ellis, R. J. Trends Biochem. Sci. 2001, 26, 597-604. (18) Shastry, M. C. R.; Eftink, M. R. Biochemistry 1996, 35, 4094-4101. (19) Meersman, F.; Dirix, C.; Shipovskov, S.; Klyachko, N. L.; Heremans, K. Langmuir 2005, 21, 3599-3604. (20) Horn, W. D. V.; Simorellis, A. K.; Flynn, P. F. J. Am. Chem. Soc. 2005, 127, 13553-13560. (21) Peterson, R. W.; Anbalagan, K.; Tommos, C.; Wand, A. J. J. Am. Chem. Soc. 2004, 126, 9498-9499. (22) Sakono, M.; Kawashima, Y.-m.; Ichinose, H.; Maruyama, T.; Kamiya, N.; Goto, M. Biotechnol. Prog. 2004, 20, 1783-1787.
10.1021/la7022902 CCC: $37.00 © 2007 American Chemical Society Published on Web 11/10/2007
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Figure 1. Schematic of the reverse micelle.
2. Interaction Potentials and Simulation Details The model and interaction potentials for the reverse micelle are similar to those used in earlier simulation studies of the Na-AOT system.14,16,23 The reverse micelle depicted schematically in Figure 1 is treated as a rigid cavity with a united atom representation for the sulfonate head group, which is held at a fixed radial distance with a harmonic potential. Because we simulate an isolated reverse micelle, periodic boundary conditions and Ewald summations for the electrostatics are not implemented. Water is treated using the extended simple point charge (SPCE) model.24 The 12-6 Lennard-Jones (LJ) parameters25 for methane are σss ) 3.73 Å and ss ) 1.226 kJ/mol. We also carried out a parametric study where σss was varied between 2.5 and 4 Å with a constant value of ss ) 0.48208 kJ/mol that is typical of the LJ energy parameter for ions such as sodium and potassium. The interaction potential, Uij, between charged species i and j (except for the hydrogen atoms in water) consists of both Coulombic and van der Waals interactions. For unlike species, the LJ potential parameters were obtained using the LorentzBerthelot mixture rules,
σij )
σii + σjj 2
and
ij ) xiijj The van der Waals interaction between a site in the interior of the reverse micelle (excluding the head groups) and the hydrocarbon region external to the headgroups is treated using a mean field approximation.14,23 All simulations were carried out for a reverse micelle of radius R ) 14.1 Å with water/ surfactant ) 4. This corresponds to 140 water molecules and 35 sodium counterions. The procedure for preparing the reverse micelle is similar to that used in earlier work.16 Monte Carlo (23) Linse, P. J. Chem. Phys. 1989, 90, 4992-5004. (24) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 19, 6269-6271. (25) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. Soc. 1984, 106, 6638-6646.
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Figure 2. (a) Methane-methane pair correlation function for two methane molecules in the reverse micelle. (b) Corresponding potential of mean force profiles. The presence of a single minimum in the potential of mean force indicates that the contact pair is the only stable configuration within the reverse micelle. The second minimum corresponding to the solvent-separated pair is not observed. The data represent averages over five independent Monte Carlo simulations whose data are shown in the insets.
simulations were carried out using the Metropolis sampling procedure. In addition to the displacement moves, the rotation of the water molecules involved a rigid body rotation around one of the three coordinate axes chosen at random.26 Interaction potentials were not truncated during the simulation. The configuration from an equilibrated reverse micelle was used as an initial configuration for adding solute atoms. The solute atoms were placed randomly in the water cavity region of the reverse micelle. Monte Carlo simulations consisted of 300 million equilibration moves followed by 200-300 million moves, during which system properties were accumulated.
3. Results and Discussion Figure 2a illustrates the pair correlation function (PCF) for two methane molecules within the reverse micelle. The corresponding potential of mean force, w(r) ) -RT ln g(r), is given in Figure 2b. The data in Figure 2 represent averages over five independent Monte Carlo simulations. Each simulation was started with a different random configuration of methane molecules. The insets illustrate the data from independent simulations. All simulations yield a single peak in the PCF; however, the peak intensities vary between simulations. The corresponding uncertainty in the well depth at the minimum in the PMF is about 1 kJ/mol. The presence of a single minimum at r ) 3.95 Å in the PMF (Figure 2b) indicates that the contact methane pair is the only stable configuration in the system and the position of the minimum is similar to that observed in other simulations of methane in bulk water.7,11,27,28 This situation is reflected as a single peak in the PCF. In all cases, the second, weaker minimum that is observed in simulations with methane7,11,27,28 and other hydrophobic solutes in bulk water7,9 is conspicuously absent. (26) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, U.K., 1987. (27) Ghosh, T.; Garcia, A. E.; Garde, S. J. Chem. Phys. 2002, 116, 24802486. (28) Trzesniak, D.; Kunz, A.-P. E.; van Gunsteren, W. F. ChemPhysChem 2007, 8, 162-169.
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Figure 3. Radial density distributions illustrating the distribution for water (oxygen), sodium counterions, and methane in the reverse micelle with two added methane molecules. The methane molecules are found to lie toward the central regions of the reverse micelle, and a depletion of the water density is observed in the central regions of the reverse micelle.
The second minimum that typically appears at r ) 7 Å for methane is associated with the presence of a solvent-separated solute pair. It is now well established for small apolar solutes such as methane that the second attractive minimum in the PMF corresponding to the solvent-separated pair reduces the loss in entropy incurred if water were to completely hydrate each separated solute entity. The second important observation is the depth of the PMF at the contact minimum when compared with simulations in the bulk. The well depth is typically around -2.0 to -3.1 kJ/mol for methane in water with the variation depending on the particular water model and solute-water interactions.7,11,27-29 In our simulations with methane, the depth of the contact minimum is -5.2 kJ/mol for two methane molecules. The near doubling of the well depth indicates a strong tendency for solute pairing under confinement. Representative radial density distributions of the methane molecules from one of the simulation runs reveal that the molecules reside within the core regions of the reverse micelle as seen in Figure 3. A decrease in water density in the central regions of the reverse micelle is observed. This is akin to a dewetting phenomenon where the water density is depleted in the regions where the contact pair is formed. To understand the stability of the solute pair, we conducted a few simulations at different temperatures. The depth of the PMF is relatively unchanged until a temperature of about 350 K is reached, indicating that the solute pair is relatively stable. Between 350 and 375 K, a lowering of the first peak of gss(r) is observed. In the case of methane11 in bulk (SPC) water, the opposite trends are observed; the well depth in the PMF corresponding to the contact pair increases, indicating that the contact pair becomes more stable as the temperature is raised between 250 and 400 K. Above 400 K, the well depth begins to decrease. This increased stabilization in the lower temperature range has been attributed in part to the negative entropy change associated with the weak solubilization of apolar solutes in water.2 We contrast our results with recent Monte Carlo and freeenergy calculations for methane confined in nanosized water droplets (1-4 nm) in hydrophobic cavities.13 In hydrophobic cavities, methane molecules are found to migrate to the surface. We observed a similar expected trend of methane molecules migrating to the surface of the reverse micelle when the charges on the headgroup were turned off in the absence of counterions. (29) Dang, L. X. J. Chem. Phys. 1994, 100, 9032-9034.
Figure 4. (a) Pair correlation functions and (b) PMF distributions for three Lennard-Jones solutes added to the reverse micelle, illustrating the effect of the solute size. The height of the peak in the pair correlation function increases monotonically with an increase in solute size. The increased tendency to form solute pairs at the larger solute size is reflected in an increase in the well depth of the PMF at the contact minimum.
Similar to our study, the PMFs in their study possess only the contact minimum; however, the depth of the minimum is only weakly negative and was found to be insensitive to the diameter of the water droplet. The presence of a single minimum in the PMF has also been observed in a recent molecular dynamics study on the collapse of hydrophobic polymers illustrating that folded or collapsed polymer states are favored for longer-chained polymers.30 3.1. Lennard-Jones Solutes. To obtain greater insight into the association tendency observed with methane, we carried out a parametric study where σss values of the LJ solutes ranged from 2.5 Å to 4.0 Å. The solute-solute PCFs, gss(r), are shown in Figure 4 where the results for all the different solute diameters at a loading of 3 solute atoms are compared. The data represent averages over two independent simulations. Unlike the case of methane, the variability between independent simulations was smaller and the trends found in Figure 4 were consistently observed. This could be a consequence of the smaller LJ energy parameter of ss ) 0.48208 kJ/mol. The main observation is the nearly 4-fold increase in the peak intensity when the solute size (30) Athawale, M. V.; Goel, G.; Ghosh, T.; Truskett, T. M.; Garde, S. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 733-738.
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is increased from σss ) 2.5 to 4.0 Å, indicating the increased probability of solute pair formation at larger solute sizes. The intensity of the tail region in the PCF decreases with an increase in solute size. The nonzero value of gss(r) at larger values of r at the smaller σss values indicates that the solute atoms are more loosely distributed within the reverse micelle. Similar qualitative trends are observed for the cases of two and four solute atoms added to the reverse micelle. In all cases, the peak values of gss(r) increase with an increase in solute size. For σss ) 2.5 Å, the radial density distributions (not shown) reveal that solute atoms are uniformly distributed in the aqueous core region (r < 10 Å) of the reverse micelle. Water in the aqueous core region of the reverse micelle is more bulk-like, whereas hydrogen bonding is significantly disrupted in the hydrophilic headgroup region.14 At larger values of σss (e.g., 3.5 Å), the solute density distribution shows a strong peak at the center of the reverse micelle and the surrounding water density is partially depleted, similar to the effect observed for methane (Figure 3). For all solute concentrations investigated in this study, the solute atoms do not populate the headgroup region of the reverse micelle where water is layered and water-water hydrogen bonding is disrupted. 3.2. Absence of Solvent-Separated Pairs. The absence of a second minimum in the PMF corresponding to the solventseparated pair for all cases studied presents a significant departure from the behavior of similar systems in bulk water. We rationalize this effect to be mainly due to the lack of sufficient free water needed to stabilize the solvent-separated state in the reverse micelle. From the methane PMF data of Lu¨deman et al.,11 where simulations were carried out for methane in SPC water, as well as from other studies of methane in water,7,27-29 the distance between the solvent-separated pair is 7 Å. Note that the values of σoo are identical for both the SPC and SPCE water models. The first minimum in the methane-oxygen PCF in our data occurred at 5.6 Å and can be used as a measure of the thickness of the first hydration shell. Using this data, the formation of the solvent-separated pair with at least one hydrated layer surrounding each solute particle requires a minimum outer distance of 18.2 Å between hydrated shells. We note that the available volume for forming one solvent-separated pair is a bare minimum requirement because a single hydrated shell cannot exist in the absence of additional water to complete the hydrogen bond network. To estimate the region where solutes are likely to be hydrated, we evaluated the hydrogen-bonding distribution as a function of the radius of the reverse micelle. Using a geometric criterion,31 the number of hydrogen bonds per water molecule is 2.8 (in the presence of 2 added methane molecules) for 0 < r < 6 Å and decreases rapidly to 0.5 at r ) 10 Å where a minimum in the water density distribution is observed (Figure 3). In contrast, the average number of hydrogen bonds in bulk SPCE water using the same geometric criterion is 3.45. We attribute the reduction in the average number of hydrogen bonds per water molecule to the lower water density in the core (0 < r < 6 Å) region of the reverse micelle. From the above estimate of 18.2 Å required to accommodate the solvent-separated pair with one fully hydrated shell, a core spherical water cavity having a radius of at least 9.1 Å is required. Because the water density and hydrogen bonding are significantly reduced for r > 6 Å, the above estimate suggests that there is (31) Guardia, E.; Laria, D.; Marti, J. J. Phys. Chem. B 2006, 110, 6332-6338.
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insufficient water to hydrate (even partially) the solvent-separated pair. In the LJ solute study with σss ) 2.5 Å (the smallest solute investigated), a similar estimate of the outer distance between hydration shells results in a distance of 15.3 Å. This results in a minimum cavity of radius 7.65 Å to support the solvated solventseparated solute configuration observed in bulk water. In our study, the greatest tendency to form the solvent-separated pair begins at σss ) 2.5 Å, where a weak shoulder is seen in the PCF around r* ) r/σss ) 2.3 (Figure 4a). The corresponding minima, albeit weak, can also be observed in the PMF (Figure 4b). From the values of σss ) 2.5 Å and σoo ) 3.16 Å, the solvent-separated minimum should occur at r ) 5.66 Å, which corresponds to a reduced radius r* ) r/σss ) 2.26. This estimate is in agreement with the location of the weak minima in the corresponding PMF seen in Figure 4b. We attribute the decreased availability of water to hydrate the solute-separated configuration as the main driving force to stabilize the contact pair configuration as the LJ solute size is increased (Figure 4).
4. Conclusions Using Monte Carlo simulations, we have evaluated the distribution of hydrophobic (Lennard-Jones) solutes in nanosized water droplets formed within the hydrophilic cavities of reverse micelles. Our results reveal a marked difference in the tendency to associate when compared with a similar situation in the bulk. The key point of departure from the extensive literature on the interaction of hydrophobic solutes in bulk water lies in the PMF. The PMFs obtained in this study, between a pair of solute molecules reveal only a single minimum, indicating that the contact configuration is the only stable configuration under confinement. The solvent-separated minimum in the PMF that is characteristic of the hydrophobic effect in bulk water is absent upon confinement. We attribute this effect mainly to the lack of sufficient water to hydrate the solutes in the solvent-separated configuration. For the case of methane, the depth of the PMF is enhanced significantly when compared with bulk water, indicating a strong enhancement of the stability of the contact pair configuration. A parametric study where the size of the LJ solute is increased, keeping the solute-solute interaction energy constant, shows that the tendency to aggregate increases with an increase in the size of the solute. In the case of methane, an increase in temperature is seen to decrease the well depth in the PMF. This study reveals that the interaction between apolar solutes in a hydrophilic cavity is markedly different from that observed for water contained in hydrophobic cavities of similar size.13 The presence of charges on the cavity wall of the reverse micelle leads to the layering of water in the vicinity of the headgroups and restricts the distribution of apolar solutes to the aqueous core regions of the reverse micelle. In contrast, apolar solutes such as methane migrate toward hydrophobic cavity walls because of van der Waals interactions.13 In conclusion, our study is important in understanding the effect of short-range hydrophobic forces on the folding of proteins as well as nucleation under confinement. These include understanding the influence of confinement and crowding effects that are present in the cell, thereby providing a more realistic cell-like environment to use in studying the aggregation and folding of proteins,17,32,33 LA7022902 (32) Lucent, D.; Vishal, V.; Pande, V. S. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 10430-10434. (33) Cheung, M.; Thirumalai, D. J. Phys. Chem. B 2007, 111, 8250-8257.
