Hydrophobic Interactions of Hexane in Nanosized Water Droplets

Aug 19, 2009 - We use all-atomistic molecular dynamics simulations to study hydrophobic interactions of hexane in nanosized water droplets where the ...
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J. Phys. Chem. B 2009, 113, 12337–12342

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Hydrophobic Interactions of Hexane in Nanosized Water Droplets Dirar Homouz, Byron Hoffman, and Margaret S. Cheung* Department of Physics, UniVersity of Houston, 4800 Calhoun Road, Houston, Texas 77204 ReceiVed: June 6, 2009

We use all-atomistic molecular dynamics simulations to study hydrophobic interactions of hexane in nanosized water droplets where the hydrogen bonding network of water molecules is disrupted at the surface. As a result of the competition between the energetics of a hexane molecule and the distribution of water molecules that lost the ability to form hydrogen bonds at the boundary, all-trans-hexane molecules are statistically favored at the surface of a nanosized water droplet and such a statistical trend increases as the size of a nano water droplet decreases. Changes in the radial distribution and the orientation of water molecules surrounding hexane in nanosized water droplets over bulk water are indicative of the finite-size effects on the structural distribution of a short, topologically complex hydrocarbon chain. Introduction Despite decades of research dedicated to hydrophobic interactions in polymers and hydrophobes,1-6 there remains a lack of molecular understanding as far as the system sizes are concerned. In a continuing march toward miniaturization where polymers can be engineered and transported in nanosized pores, new ideas and concepts are demanded for understanding chemical interactions in a nanocontainer7 that can accommodate only a few hundred atoms at a time. One prominent example is protein folding, an event largely driven by the collapse8 of hydrophobic residues in water. In the presence of confinement,7,9,10 compact conformations of a folded protein are favored because the pore sizes restrict the extended conformations. However, it was also shown that the finite-size effects can favor unfolded proteins if the behavior of confined water molecules is taken into account.11 The question is then how confinement effects dictate the competition for space between water molecules and biopolymers in which the arrangement of the former in turn affects the structural complexity of the latter. The investigation of these aspects of the hydrophobic effect is important in studying the conformations of sol-gel encapsulated proteins12 as well as chemical reactions in the cell where bimolecular interactions take place in highly crowded or confined spaces.13 It may also be pertinent to understanding the mechanism to drive crude hydrocarbons out of small pores in aquifers in the process of enhanced oil recovery.14 Oil residues in nanosized water droplets are unlikely to form the aggregates they adopt in bulk water. Using methane as a model for studying hydrophobic interactions in a confined space,15 it was shown that interactions between methanes in nanosized pores are not statistically favored. Methanes are located at the surface of a water droplet where the hydrogen bond network of water molecules is severed. This investigation sparked new questions about the confinement effect on the hydrogen bonding of water molecules and on the hydrophobic interaction in topologically complex hydrocarbons. Answers to such questions are crucial to applications in nanobiotechnology. However, such an issue has not been studied thoroughly. * Corresponding author. Phone: (713)743-8358. Fax: (713) 743- 3589. E-mail: [email protected].

Decades of computer simulation and analytical studies have been devoted to advancing the understanding of the arrangement of water molecules surrounding hydrocarbon polymers with various sizes and lengths. Calculations of the entropy of hydration of n-alkanes have been carried out to characterize their dominant ensemble conformations in bulk water.16 Several previous studies have shown that water molecules organize themselves into clathrate-like structures around different sizes and topologies of nonpolar solutes.3,17-20 These findings suggest that the conformations of hydrocarbon polymers can in turn be altered by the hydrophobic interactions in the presence of an excessive amount of water molecules. Other studies have focused sharply on the chemically compact forms of hydrocarbons such as cyclohexane and benzene in bulk water to investigate the effects of complex topography on the orientation of proximal water molecules.21 However, the extent to which the hydrophobic interactions will change in a nanosized water droplet remains unknown and is the focus of this work. We use all-atomistic molecular simulations with explicit solvent molecules on hexane in several nanosized water droplets as well as under bulk conditions at T ) 300K (see the Methods section). The water molecules and hexane in a droplet are confined by spherical boundary conditions. The diameter of the smallest water droplet is within the length scale of an all-trans-hexane; therefore, deformation of a hexane molecule due to space restriction is unlikely to happen in our study. Methods Molecular Simulations. Molecular dynamics simulations based on the NAMD package22 were used to study the thermodynamic properties of a single hexane molecule in aqueous solution and in nanosized water droplets (Table 1). A cubic box of 4.4 nm × 4.4 nm × 4.4 nm with periodic boundary conditions was prepared for the simulations under bulk conditions. Spherical boundary conditions (SBC) at the surface of a water droplet were used to prevent water molecules from escaping the droplets (Figure 1). Spherical boundary conditions (SBC) at the surface of a water droplet were used to prevent water molecules from escaping the droplets (Figure 1). In SBC, the confining energy of an atom at a distance r from the origin is y(r) ) k(r - ro)2, when r g ro, ro is the radius of the

10.1021/jp907318d CCC: $40.75  2009 American Chemical Society Published on Web 08/19/2009

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TABLE 1: Number of Water Molecules and the Water Density for a Given Simulation System system

size

sphere sphere sphere sphere periodic cubic box

2.0 nm diameter 2.0 nm diameter 2.0 nm diameter 4.0 nm diameter 4.4 nm × 4.4 nm × 4.4 nm

water density (g/cm3)

no. of water molecules

0.73 1.00 1.26 1.00 1.00

103 140 177 1169 2728

spherical pore and k is 5 kcal/mol/Å2, while y(r) ) 0 at r < ro. Given this confining potential, interactions between the molecules and the wall of a pore are repulsive. The diameter of a spherical water droplet ranges from 2.0 to 4.0 nm. Water molecules are represented by the TIP3P model,23 and the CHARMM24 force field and its derivatives are used for interactions in hexane.25 Preparation of each system starts by energy minimization using the conjugate gradient method, followed by 500 ps of equilibration at a range of temperatures needed for the production simulations that implement the replica exchange method (REM).26 The RATTLE algorithm is used to keep a fixed bond length in all bonds, and the integration time step is 2.0 fs. The replica exchange method is used to enhance the sampling efficiency of molecular dynamics. Sixteen copies (replicas) of molecular dynamics were simulated at temperatures ranging from 280 to 400 K. For each replica (copy), a molecular dynamics simulation was performed at constant volume and temperature (NVT) where the heat bath is maintained by Langevin thermostat. A total of 50 Metropolis exchanges are attempted every 200 ps for all replicas. We gathered the configurations sampled from the 16 (10 ns) simulations and use the weighted histogram analysis method (WHAM)27,28 to analyze the free energy and thermodynamic averages. Characterization of the Water Structure. Water Density Profile. We measured the water density profile surrounding a hexane carbon as a function of the radial distance, r, from that carbon atom. We calculated the number of water molecules in a spherical shell of thickness ∆ ) 0.1 Å with radius r centered at one carbon atom. This number is divided by the volume of the shell inside the water nanopore in order to get the water density in that shell. Water Orientation. The orientation of water molecules is defined by the cosine of the angle (θ) between two vectors CO and OH (either OH1 or OH2). CO is a vector pointing from a hexane carbon to the water oxygen atom. OH is a vector from the water oxygen atom to a water hydrogen atom (H1 or H2).

Figure 1. All-atomistic representation of a hexane molecule in a spherical water droplet of 4 nm diameter.

Figure 2. (A) Free energy of a hexane molecule as a function of the distance, r, between its center of mass and the center position of a spherical water droplet. Hexane molecules in water droplets of 2.0 nm (solid line), 3.0 nm (dotted line), and 4.0 nm (dashed line) diameter are given. (B) The free energy using the same x-axis as that in part A is computed for hexane in a spherical water droplet of 2.0 nm diameter (D ) 2.0 nm) under different water densities: 0.73 g/cm3 (solid), 1.0 g/cm3 (dashed), and 1.26 g/cm3 (dotted). Error bars are included.

Clustering Analysis. The dominant hexane configurations were determined using a clustering method that is based on a self-organized neural net algorithm.10 It characterizes the structural distribution without prior knowledge of an ensemble. Each hexane conformation j is described by a 10-dimensional vector xj, whose elements are the distance between each pair of carbon atoms in that conformation. The conformations in an ensemble are first sorted randomly into different clusters each with index k. The center of mass of each cluster k will be then defined as (∑j xj)/Nk, where Nk is the number of conformations in the cluster. Conformation j is sorted to the kth cluster if the Euclidean distance between conformation j and the center of mass of the kth cluster is shorter than a cutoff. Adding conformations to any cluster will update its center of mass. This process reiterates itself accompanied by addition or deletion of new elements into each cluster until the centers of masses of all clusters converge. The cutoff distance used in this work is 1.45 Å. Results and Discussion The Favorable Position of a Hexane Molecule Is at the Surface of a Nano Water Droplet. We used all-atomistic molecular dynamics simulations on a hexane molecule in the bulk water and in spherical water droplets of 2.0-4.0 nm diameter to investigate the confinement effects on the structural distribution of hexane. An illustration of a hexane molecule in a spherical water droplet is shown in Figure 1. The simulations show that hexane is more likely to be near the surface of the droplets rather than the interior (Figure 2). Noticeably, in a water droplet of 4.0 nm diameter, the difference in the free energy minima between a hexane molecule near the surface and at the interior position is approximately equal to the hydration free energy experimentally measured for hexane under bulk conditions which is about 2.58 kcal/mol.29 This free energy difference grows to about 5 kcal/mol as the diameter of the water droplet is reduced to 2.0 nm. Thus, the free energy cost to relocate a hexane molecule from the surface to an interior position in the smaller water droplet increases to about twice the hydration energy of hexane in bulk water, indicating that the attraction between hexane and the wall of a pore increases as the pore size decreases. The reason lies in the broken hydrogen bonds among water molecules at the surface of a water droplet caused by confinement. A hexane molecule statistically favors the surface position because such an arrangement minimizes the disruption of water molecules in the interior of the droplet and has little effect on the already severed hydrogen bonding network at the surface. When the pore size

Hydrophobic Interactions of Hexane

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Figure 3. (A) Free energy of a hexane molecule as a function of its end-to-end distance, d, between C1 and C6 atoms in the following systems: bulk water (sold line), a spherical water droplet of 2.0 nm diameter (dash-dotted line), and a spherical water droplet of 4.0 nm diameter (dotted line). Arrows point to different minima in the free energy profile populated by (a) ttt, (b) tgt, and (c) ggg hexane. The water density is 1.0 g/cm3 in the above conditions. (B) The free energy of a hexane molecule as a function of d in a spherical droplet of a 2.0 nm diameter with different water densities: 0.73 g/cm3 (solid line), 1.0 g/cm3 (dash-dotted line), and 1.26 g/cm3 (dotted line).

TABLE 2: Percentage of Dominant Clusters of Hexane Conformations in Water Droplets of 2.0 and 4.0 nm as well as in Bulk Water system

ttt

tgt

ggg

2.0 nm water droplet 4.0 nm water droplet bulk water

36% 36% 27%

18% 18% 17%

29% 42% 43%

decreases, the disruption of the hydrogen bonding network at the surface is greater, causing the overall attraction between hexane and the wall to become stronger. These observations for hexane agree with previous studies on methane molecules15 in nanosized water droplets. However, hexane is topologically more complex than methane and such a complexity results in subtle differences in their free energy profiles, as shown in Figure 2. We find that the width of the free energy minimum in larger pores is greater than that in smaller ones, indicating that hexane may adopt a broader structural distribution of ensemble conformations in larger pores. Dominant Conformations of a Hexane Molecule Depend on the Sizes of Nano Water Droplets. We plot the free energy profile as a function of an end-to-end distance of a hexane molecule (a distance between the C1 and C6 atom), d, in several water droplets in Figure 3 in order to investigate the size effects on the conformational changes in hexane. The figure shows that the free energies of hexane in the bulk water and water droplets (of 2.0 and 4.0 nm diameter) share the same positions of free energy minima at d ) 0.55, 0.6, and 0.64 nm. However, their statistical weighting distributed among these minima differs noticeably. We therefore applied a self-organized neural net clustering algorithm10 (see Methods) to characterize the dominant hexane conformations corresponding to each minimum in Figure 3A. The dominant structures corresponding to the minima of d ) 0.55, 0.60, and 0.64 nm are ggg, tgt, and ttt hexanes (t, trans; g, gauche), respectively. The population of the ttt conformation increases relative to the ggg conformation as the size of the droplet is decreased (Table 2). Conformational entropy changes in hexane are not likely to happen in the pores used in our simulation, as their sizes are greater than the length of an extended hexane. The major cause of the shift in the free energy with respect to the size of confinement can be explained in terms of the competition between the energetics of hexane and the entropy of water molecules. In bulk water, the entropy of hydrogen bonding is maximized when hexane adopts a more compact form (e.g., ggg hexane) which gives a smaller surface

area in contact with water molecules, although this gauche conformation is unlikely to achieve the lowest energy of hexane. However, when hexane is positioned in a nano water droplet, the surface solvation will relieve the strain of energetics by allowing a ttt-hexane at the surface, reducing the population of ggg-hexane. The Effect of Water Density in Nano Droplets Confined in a Pore on Hexane Conformations. We next investigated the effects of changing the water density on hexane in nanosized water droplets confined in a spherical pore using the free energy profile as a function of the position of hexane inside the pore (Figure 2B). The width of the free energy minimum near the surface grows when the water density decreases from 1.26 to 0.73 g/cm3. In addition, the broadening of the width in the free energy minimum near the surface indicates that there are noticeable changes in the distribution of hexane conformations. Hence, we further plotted the free energy profile as a function of the end-to-end distance in Figure 3B, and found that ggg conformations are more populated at lower water densities. On the other hand, when the water density exceeds 1 g/cm3, the width of the free energy minimum at the surface of a droplet narrows (Figure 2B), attributed to an increased population of ttt-hexane (Figure 3B). Radial Distribution Function of Water Molecules Surrounding a Hexane Carbon in Nano Water Droplets. It is known that the radial distribution function and the orientation of water molecules depend on the molecular topology and the size of a hydrophobic surface.17,19,21 However, how water molecules organize themselves around a topologically complex hydrocarbon such as hexane in nanosized water droplets is a question that has not been investigated. We first studied the distribution of water molecules surrounding carbon atoms in a hexane molecule using the water density profiles in Figure 4. The first peak position for the C1 atom (C1 is the terminal carbon in hexane) at r ∼0.35 nm agrees with the peak position of the first hydration shell for methanes.18 However, the first peak positions for C2 and C3 are located at a greater value (r ∼0.5 nm) due to the excluded volume of the neighboring carbon atoms which block the access of water molecules. When we compare the water density profiles for different confining conditions, we find that the peak amplitude for C1 is lower in water droplets than that in bulk water. It is partly due to the fact that reducing the pore size will increase the population of ttt conformations, which changes the structure of water around hexane. In an all-trans configuration, all carbon atoms become equivalently accessible to water molecules. In addition, lower peak amplitude in C1 is also attributed to the poor structure of water in confinement, as will be discussed in the next section. Water Orientation Surrounding Hexane in Nano Water Droplets. In bulk water, the orientation of water molecules surrounding a hydrophobic surface is determined by two competing factors: the packing forces which result in a dense layer in contact with the surface and the trend of water molecules to achieve the maximal number of hydrogen bonds.19 However, in this work, the existence of a topologically complex hydrocarbon in a finite-size system will limit the options for hydrogen bonding between water molecules. Therefore, the orientations of water molecules surrounding hexane may be different from those in bulk water. We measure the orientation of proximal water molecules using the cosine of an angle, θ, between the CO vector (pointing from C to O) and the OH1 (or OH2) vector. The distribution of cos(θ) of water molecules within 0.4 nm of a carbon atom

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Figure 4. Water density, Fwater, at a distance, r, away from a carbon atom in a hexane molecule: C1 (solid line), C2 (dashed line), and C3 (dotted line), where C1 is the terminal atom. Several conditions are considered: (A) bulk water, (B) a spherical water droplet of 2.0 nm diameter, and (C) a spherical water droplet of 4.0 nm diameter.

Homouz et al. water droplet, the average orientation of water molecules surrounding the C1 position is different from than in the bulk. Although the major peaks are still centered at cos(θ) ) -0.33 and 1, the population of another orientation of the water molecules with θ ) 180° (cos(θ) ) -1) increases noticeably. These water molecules have one hydrogen bond pointing toward the carbon atom, and the orientation is inverted relative to the clathrate-like water structures. This notion becomes evident as the pore size reduces. It suggests that, in the presence of confinement, water molecules may be forced to give up one hydrogen bond in order to pack at the hydrophobic surface; thus, the inverted water molecules are found to solvate around the complex topology of hexane. This compromised water arrangement may explain the reduction of peak amplitude in the water density along C1 in Figure 4. In order to get better insight into the water structure surrounding a C1 atom in hexane, we plot the water distribution using the two parameters: the radial distance, r, between a C1 atom in hexane and an oxygen in proximal water molecules and a relative water orientation represented by cos(θ). Figure 6A shows the distribution of r and cos(θ) in bulk. There are two broad peaks around cos(θ) ) 1 and -0.33 (or θ ) 0 and 109°) within the first hydration shell around r ) 0.4 nm. The effects of confinement can be clearly shown by the difference of the water distribution profile between the bulk water and nanosized water droplets of 2.0 nm diameter (Figure 6B) and 4.0 nm diameter (Figure 6C). Blue areas marked a decrease in water molecules with clatherate-like structures surrounding C1 in the presence of confinement. An increased area in red suggests that the distribution of water molecules is broader inside water droplets compared to bulk water. Conclusions

in a hexane is shown in Figure 5. The two peaks in the distribution correspond to the two tetrahedral angles of θ ) 109 and 0° (cos(θ) ) -0.33 and 1), showing that water molecules organize themselves in a clatharate-like structure in the proximity of hexane in bulk water. However, in a nanosized

Through the lens of polymer theory, confinement and macromolecular crowding may favor compact native states because the distributions of extended protein configurations are restricted inside a pore.9,30-32 Confinement can also influence the arrangement of water molecules which in turn affects the

Figure 5. Probability distribution of the water orientation around a carbon atom in hexane under the following conditions: (A) bulk water, (B) a spherical water droplet of 2.0 nm diameter, and (C) a spherical water droplet of 4.0 nm. Each panel shows the probability distribution around three carbon atoms, respectively: C1 (solid line), C2 (dashed line), and C3 (dotted line). (D) This schematic diagram shows a typical organization of two water molecules surrounding a hydrophobic solute in a clathrate-like structure. The two most probable orientations of the angles θ (0 and 109°) are shown on this diagram.

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J. Phys. Chem. B, Vol. 113, No. 36, 2009 12341 and the TcSUH seed grant from the University of Houston. We are grateful to Drs. S. Vaitheeswaran, D. Thirumalai, and T. Truskett for useful comments and references. A critical reading of this manuscript by Dr. Hank Ashbaugh is greatly appreciated. References and Notes

Figure 6. (A) Probability distribution of the distance, r, between O in the proximal waters and C1 in hexane and their corresponding angular orientation between OH and OC1 in terms of cos(θ) in bulk water. (B, C) The difference in the probability distribution between the bulk water and that in water droplets of 2.0 and 4.0 nm diameter, respectively, is plotted using the same x- and y-axes. The contours are added for visual guidance.

hydrophobic interactions in topologically complex hexane. In conclusion, we have shown that a ttt-hexane is statistically favored in nanosized water droplets because of the disruption of the hydrogen bonding in water molecules at the surface of a droplet. This study provides better insights into experimental studies on protein folding in a confined or crowded space such as the cell where water is unlikely to behave as bulk water and would play an active role in biological functions.13,33 Acknowledgment. D.H. and M.S.C. would like to thank Buddhi Tilakaratne, Qian Wang, Antonios Samiotakis, and Dr. Samina Masood for valuable discussions. M.S.C. would like to thank TeraGrid and TLC2 for the computing resources, as well as the UH GEAR grant, the ACS Petroleum Research Fund,

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