Towards an understanding of the molecular basis of hydrophobicity

Summary The modern view is stressed that the structuring of water around nonpolar solutes, a process called hydrophobic hydration, actually favors the solubility of nonpolar solutes in water, its associated positive free energy of transfer arising from the enthalpic input required to create a cavity in water to accommodate the solute. The results of a series of molecular dynamics simulations of methane in SPC/E water at different temperatures are reported. These results show the existence of a larger fraction of broken hydrogen bonds in the hydration-shell water of the nonpolar solutes with respect to the bulk water, the difference increasing with a rise in temperature. This supports Muller's modified hydration-shell hydrogen-bond model predictions, where hydration-shell water molecules have lower free energies of hydrogen-bond breaking than those in the bulk.This paper is based on a presentation given at the 14th Molecular Graphics and Modelling Society Conference, held in Cairns, Australia, August 27 September 1, 1995.     

Effect of solute size and solute-water attractive interactions on hydration water structure around hydrophobic solutes.

Using Monte Carlo simulations, we investigated the influence of solute size and solute-water attractive interactions on hydration water structure around spherical clusters of 1, 13, 57, 135, and 305 hexagonally close-packed methanes and the single hard-sphere (HS) solute analogues of these clusters. We obtain quantitative results on the density of water molecules in contact with the HS solutes as a function of solute size for HS radii between 3.25 and 16.45 A. Analysis of these results based on scaled-particle theory yields a hydration free energy/surface area coefficient equal to 139 cal/(mol A2), independent of solute size, when this coefficient is defined with respect to the van der Waals surface of the solute. The same coefficient defined with respect to the solvent-accessible surface decreases with decreasing solute size for HS radii less than approximately 10 A. We also find that solute-water attractive interactions play an important role in the hydration of the methane clusters. Water densities in the first hydration shell of the three largest clusters are greater than bulk water density and are insensitive to the cluster size. In contrast, contact water densities for the HS analogues of these clusters decrease with solute size, falling below the bulk density of water for the two largest solutes. Thus, the large HS solutes dewet, while methane clusters of the same size do not.     

How hydrophobic buckminsterfullerene affects surrounding water structure

The hydrophobic hydration of fullerenes in water is of significant interest as the most common Buckminsterfullerene (C60) is a mesoscale sphere; C60 also has potential in pharmaceutical and nanomaterial applications. We use an all-atom molecular dynamics simulation lasting hundreds of nanoseconds to determine the behavior of a single molecule of C60 in a periodic box of water, and compare this to methane. A C60 molecule does not induce drying at the surface; however, unlike a hard sphere methane, a hard sphere C60 solute does. This is due to a larger number of attractive Lennard-Jones interactions between the carbon atom centers in C60 and the surrounding waters. In these simulations, water is not uniformly arranged but rather adopts a range of orientations in the first hydration shell despite the spherical symmetry of both solutes. There is a clear effect of solute size on the orientation of the first hydration shell waters. There is a large increase in hydrogen-bonding contacts between waters in the C60 first hydration shell. There is also a disruption of hydrogen bonds between waters in the first and second hydration shells. Water molecules in the first hydration shell preferentially create triangular structures that minimize the net water dipole near the surface near both the methane and C60 surface, reducing the total energy of the system. Additionally, in the first and second hydration shells, the water dipoles are ordered to a distance of 8 A from the solute surface. We conclude that, with a diameter of approximately 1 nm, C60 behaves as a large hydrophobic solute.     

On the molecular origins of volumetric data

We use a statistical thermodynamic approach and a simple thermodynamic model of hydration to examine the molecular origins of the volumetric properties of solutes. In this model, solute-solvent interactions are treated as a binding reaction. The free energy of hydration of the noninteracting solute species coincides with the free energy of cavity formation, while the free energy of solute-solvent interactions is given by the binding polynomial. By differentiating the relationship for the free energy of hydration with respect to temperature and pressure, one obtains the complete set of equations describing the thermodynamic profile of hydration, including enthalpy, entropy, volume, compressibility, expansibility, and so forth. The model enables one to rigorously define in thermodynamic terms the hydration number and the related concept of hydration shell, which are both widely used as operational definitions in experimental studies. Hydration number, nh, is the effective number of water molecules solvating the solute and represents the derivative of the free energy of hydration with respect to the logarithm of water activity. One traditional way of studying hydration relies on the use of volumetric measurements. However, microscopic interpretation of macroscopic volumetric data is complicated and currently relies on empirical models that are not backed by theory. We use our derived model to link the microscopic determinants of the volumetric properties of a solute and its statistical thermodynamic parameters. In this treatment, the partial molar volume, V degrees, of a solute depends on the cavity volume, hydration number, and the properties of waters of hydration. In contrast, the partial molar isothermal compressibility, K degrees T, and expansibility, E degrees, observables, in addition to the intrinsic compressibility and expansibility of the cavity enclosing the solute, hydration number, and the properties of waters of hydration, contain previously unappreciated relaxation terms that originate from pressure- and temperature-induced perturbation of the equilibrium between the solvated solute species. If significant, the relaxation terms may bring about a new level of nonadditivity to compressibility and expansibility group contributions that goes beyond the overlap of the hydration shells of adjacent groups. We apply our theoretical results to numerical analyses of the volume and compressibility responses to changes in the distribution of solvated species of polar compounds.     

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. IV. Pairs of different hydrophobic side chains

The potentials of mean force of 21 heterodimers of the molecules modeling hydrophobic amino acid side chains: ethane (for alanine), propane (for proline), isobutane (for valine), isopentane (for leucine and isoleucine), ethylbenzene (for phenylalanine), methyl propyl sulfide (for methionine), and indole (for tryptophane) were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation. Analytical expressions consisting of the Gay-Berne term to represent effective van der Waals interactions and the cavity term proposed in our earlier work were fitted to the potentials of mean force. The positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the orientation of the molecules, are well represented by the analytical expressions for all systems; large deviations between the MD-determined PMF and the analytical approximations are observed for pairs involving the least spheroidal solutes: ethylbenzene, indole, and methyl propyl sulfide at short distances at which the PMF is high and, consequently, these regions are rarely visited. When data from the PMF within only 10 kcal/mol above the global minimum are considered, the standard deviation between the MD-determined and the fitted PMF is from 0.25 to 0.55 kcal/mol (the relative standard deviation being from 4% to 8%); it is larger for pairs involving nonspherical solute molecules. The free energies of contact computed from the PMF surfaces are well correlated with those determined from protein-crystal data with a slope close to that relating the free energies of transfer of amino acids (from water to n-octanol) to the average contact free energies determined from protein-crystal data. These observations justify future use of the determined potentials in coarse-grained protein-folding simulations.     

Cavitation free energy for organic molecules having various sizes and shapes

Cavitation free energy DeltaG(cav), corresponding to the formation of an excluded volume cavity in water, is calculated for a large set of organic molecules employing the thermodynamic integration procedure, which is realized as the original two-step algorithm for growing the interaction potential between the hard cavity wall and the water molecules. A large variety of solute systems is considered. Their characteristic radii change in the range 3-7 A; spherical cavities with radii 3-6 A are also studied. The interaction between water molecules is described by the four-site nonpolarizable TIP4P model. The diversity of the trial molecular set is provided by using a specially formulated nonspherical criterion classifying the cavity shapes according to their deviation from a sphere. Molecular objects were partly taken from the data base NCI Diversity with the aid of this criterion. The so-computed free energies are approximated by the linear volume dependence DeltaG(cav)V = XiV, where V is the cavity volume. This relation works fairly well until the cavity size becomes very large (the effective radius larger than 7 A). The volume dependence valid for solutes of arbitrary shapes can be included in a calculation of the nonpolar free energy component as required in the implicit water model.     

Water coordination structures and the excess free energy of the liquid

We assess the contribution of each coordination state to the hydration free energy of a distinguished water molecule, the solute water. We define a coordination sphere, the inner-shell, and separate the hydration free energy into packing, outer-shell, and local, solute-specific (chemical) contributions. The coordination state is defined by the number of solvent water molecules within the coordination sphere. The packing term accounts for the free energy of creating a solute-free coordination sphere in the liquid. The outer-shell contribution accounts for the interaction of the solute with the fluid outside the coordination sphere and it is accurately described by a Gaussian model of hydration for coordination radii greater than the minimum of the oxygen-oxygen pair-correlation function: theory helps identify the length scale to parse chemical contributions from bulk, nonspecific contributions. The chemical contribution is recast as a sum over coordination states. The nth term in this sum is given by the probability p(n) of observing n water molecules inside the coordination sphere in the absence of the solute water times a factor accounting for the free energy, W(n), of forming an n-water cluster around the solute. The p(n) factors thus reflect the intrinsic properties of the solvent while W(n) accounts for the interaction between the solute and inner-shell solvent ligands. We monitor the chemical contribution to the hydration free energy by progressively adding solvent ligands to the inner-shell and find that four-water molecules are needed to fully account for the chemical term. For a chemically meaningful coordination radius, we find that W(4) ≈ W(1) and thus the interaction contribution is principally accounted for by the free energy for forming a one-water cluster, and intrinsic occupancy factors alone account for over half of the chemical contribution. Our study emphasizes the need to acknowledge the intrinsic solvent properties in interpreting the hydration structure of any solute, with particular care in cases where the solute-solvent interaction strength is similar to that between the solvent molecules.     

Molecular origin of anticooperativity in hydrophobic association

The structuring of water molecules in the vicinity of nonpolar solutes is responsible for hydrophobic hydration and association thermodynamics in aqueous solutions. Here, we studied the potential of mean force (PMF) for the formation of a dimer and trimers of methane molecules in three specific configurations in explicit water to explain multibody effects in hydrophobic association on a molecular level. We analyzed the packing and orientation of water molecules in the vicinity of the solute to explain the effect of ordering of the water around nonpolar solutes on many-body interactions. Consistent with previous theoretical studies, we observed cooperativity, manifested as a reduction of the height of the desolvation barrier for the trimer in an isosceles triangle geometry, but for linear trimers, we observed only anticooperativity. A simple mechanistic picture of hydrophobic association is drawn. The free energy of hydrophobic association depends primarily on the difference in the number of water molecules in the first solvation shell of a cluster and that in the monomers of a cluster; this can be approximated by the molecular surface area. However, there are unfavorable electrostatic interactions between the water molecules from different parts of the solvation shell of a trimer because of their increased orientation induced by the nonpolar solute. These electrostatic interactions make an anticooperative contribution to the PMF, which is clearly manifested for the linear trimer where the multibody contribution due to changes in the molecular surface area is equal to zero. The information theory model of hydrophobic interactions of Hummer et al. also explains the anticooperativity of hydrophobic association of the linear trimers; however, it predicts anticooperativity with a qualitatively identical distance dependence for nonlinear trimers, which disagrees with the results of simulations.     

Evaluation of the contribution to hydration of nonelectrolytes from the hydrophobic effect

A new method was suggested for estimating the hydrophobic effect of contributions to the Gibbs energies and enthalpies of hydration of hydrocarbons, inorganic gases and rare gases. In accordance with this method the hydrophobic effect contribution to the Gibbs energy was evaluated from the difference between the hydration Gibbs energy of a solute and the non hydrophobic contribution. To estimate the latter value, the known dependence connecting the Gibbs energies of solvation of a solute in a number of aprotic solvents to the Hildebrand solubility parameter for these solvents was used. The non hydrophobic contribution to the Gibbs energy of hydration was calculated for various solutes from such dependences extended to water as solvent. The Hildebrand solubility parameter for water used in the calculation was corrected for the effect of association through hydrogen bonding. This correction was made by subtraction of the water self-association enthalpy from the enthalpy of vaporization of water. The evaluated Gibbs energies of the hydrophobic effect are positive for saturated hydrocarbons, inorganic gases and rare gases and linearly depend on the solute molecular refraction. The hydrophobic contribution to the hydration enthalpies of the solutes was calculated in the same manner as was made to calculate the hydrophobic contribution to Gibbs energies of hydration. Enthalpies of the hydrophobic effect for the solutes under study are negative.     

Hydration of hydrophobic solutes treated by the fundamental measure approach

We have developed a method to calculate the hydration of hydrophobic solutes by the fundamental measure theory. This method allows us to carry out calculations of the density profile and the hydration energy for hydrophobic molecules. An additional benefit of the method is the possibility to calculate interaction forces between solvated nanoparticles. Based on the designed method, we calculate hydration of spherical solutes of various sizes from one angstrom up to several nanometers. We have applied methods to evaluate the free energies, the enthalpies, and the entropies of hydrated rare gases and hydrocarbons. The obtained results are in agreement with available experimental data and simulations.     

The Hydrophobic Effects: Our Current Understanding

Hydrophobic interactions are involved in and believed to be the fundamental driving force of many chemical and biological phenomena in aqueous environments. This review focuses on our current understanding on hydrophobic effects. As a solute is embedded into water, the interface appears between solute and water, which mainly affects the structure of interfacial water (the topmost water layer at the solute/water interface). From our recent structural studies on water and air-water interface, hydration free energy is derived and utilized to investigate the origin of hydrophobic interactions. It is found that hydration free energy depends on the size of solute. With increasing the solute size, it is reasonably divided into initial and hydrophobic solvation processes, and various dissolved behaviors of the solutes are expected in different solvation processes, such as dispersed and accumulated distributions in solutions. Regarding the origin of hydrophobic effects, it is ascribed to the structural competition between the hydrogen bondings of interfacial and bulk water. This can be applied to understand the characteristics of hydrophobic interactions, such as the dependence of hydrophobic interactions on solute size (or concentrations), the directional natures of hydrophobic interactions, and temperature effects on hydrophobic interactions.     

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. 2. Tests with simple spherical systems

Simple analytical functions consisting of electrostatic, polarization, Lennard-Jones or modified Lennard-Jones, and cavity terms are proposed to express the potentials of mean force analytically for spherical particles interacting in water. The cavity term was expressed either through the molecular-surface area of the solute or by using the Gaussian-overlap model of hydrophobic hydration developed in paper 1 of this series. The analytical expressions were fitted to the potentials of mean force of a methane homodimer, heterodimers composed of a methane molecule, and an ammonium cation or a chloride anion, respectively, and dimers consisting of two chloride anions, two ammonium cations, or a chloride ion and an ammonium cation. The potentials of mean force for these dimers were determined by umbrella-sampling molecular dynamics simulations with the AMBER 7.0 force field with TIP3P water either in our earlier work or in this work. For all systems, the analytical formulas fitted the potentials of mean force very well. However, using the molecular-surface area to express the cavity term provided a good fit only when the nonbonded interactions were expressed by an all-repulsive modified Lennard-Jones potential but also resulted in non-physical values of some of the parameters. Conversely, the use of our new Gaussian-overlap-based expression for the cavity term provided a good fit to the potentials of mean force (PMFs) with Lennard-Jones nonbonded potential, and the values of all parameters were physically reasonable.     

A method for calculating the Gibbs energies of hydrophobic effects and specific interactions of nonelectrolytes in aqueous solutions

The thermodynamic characteristics of hydrophobic hydration, the Gibbs energies of hydrophobic effect, were calculated. The method for calculations was based on the division of the Gibbs energy of hydration into contributions of nonspecific interactions, specific interactions between solutes and solvents (if they exist), and hydrophobic effect. In the absence of specific interactions between solutes and water, the Gibbs energy of hydrophobic effect depended linearly on the characteristic molecular volume of the solute for substances with different structures and properties. The universality of this dependence allows the suggestion to be made that it remains valid also in the presence of specific interactions. This allows the Gibbs energy of specific interactions in water to be determined for a wide range of compounds, in particular, for aliphatic alcohols.     

Solutes probe hydration in specific association of cyclodextrin and adamantane

Using microcalorimetry, we follow changes in the association free energy of beta-cyclodextrin (CD) with the hydrophobic part of adamantane carboxylate (AD) due to added salt or polar (net-neutral) solutes that are excluded from the molecular interacting surfaces. Changes in binding constants with solution osmotic pressure (water activity) translate into changes in the preferential hydration upon complex formation. We find that these changes correspond to a release of 15-25 solute-excluding waters upon CD/AD association. Reflecting the preferential interaction of solute with reactants versus products, we find that changes in hydration depend on the type of solute used. All solutes used here result in a large change in the enthalpy of the CD-AD binding reaction. In one class of solutes, the corresponding entropy change is much smaller, while in the other class, the entropy change almost fully compensates the solute-specific enthalpy. For many of the solutes, the number of waters released correlates well with their effect on air-water surface tensions. We corroborate these results using vapor pressure osmometry to probe individually the hydration of reactants and products of association, and we discuss the possible interactions and forces between cosolute and hydrophobic surfaces responsible for different kinds of solute exclusion.     

Thermal signature of hydrophobic hydration dynamics

Hydrophobic hydration, the perturbation of the aqueous solvent near an apolar solute or interface, is a fundamental ingredient in many chemical and biological processes. Both bulk water and aqueous solutions of apolar solutes behave anomalously at low temperatures for reasons that are not fully understood. Here, we use (2)H NMR relaxation to characterize the rotational dynamics in hydrophobic hydration shells over a wide temperature range, extending down to 243 K. We examine four partly hydrophobic solutes: the peptides N-acetyl-glycine-N'-methylamide and N-acetyl-leucine-N'-methylamide, and the osmolytes trimethylamine N-oxide and tetramethylurea. For all four solutes, we find that water rotates with lower activation energy in the hydration shell than in bulk water below 255 +/- 2 K. At still lower temperatures, water rotation is predicted to be faster in the shell than in bulk. We rationalize this behavior in terms of the geometric constraints imposed by the solute. These findings reverse the classical "iceberg" view of hydrophobic hydration by indicating that hydrophobic hydration water is less ice-like than bulk water. Our results also challenge the "structural temperature" concept. The two investigated osmolytes have opposite effects on protein stability but have virtually the same effect on water dynamics, suggesting that they do not act indirectly via solvent perturbations. The NMR-derived picture of hydrophobic hydration dynamics differs substantially from views emerging from recent quasielastic neutron scattering and pump-probe infrared spectroscopy studies of the same solutes. We discuss the possible reasons for these discrepancies.     

Hydration of aprotic donor solvents studied by means of FTIR spectroscopy

The paper attempts to explain the mutual influence of nonpolar and electron-donor groups on solute hydration, the problem of big importance for biological aqueous systems. Aprotic organic solvents have been used as model solutes, differing in electron-donating power. Hydration of acetonitrile, acetone, 2-butanone, and triethylamine has been studied by HDO and (partially) H2O spectra. The quantitative version of difference spectra method has been applied to determine solute-affected water spectra. Analysis of the data suggests that solvent-water interaction via the donor center of the solute is averaged between water-water interactions around the solute. Such behavior can be simply explained by the model of solute rotating in a cavity of water structure, which is formed by clathratelike hydrogen-bonded water network. On the basis of the band shape of solute-affected HDO spectra and the corresponding distribution of intermolecular distances, the criterion for hydrophobic type hydration has been proposed. From that point of view, all the studied solutes could be treated as hydrophobic ones. The limiting band position and the corresponding intermolecular distance of affected water, gained with increasing electron-donating power of solutes, has been inferred from the data obtained. These observations are important for interpretation of vibrational spectra of water as well as for volumetric measurements of solutions. The simple model of hydration, proposed to better justify the results, connects the values obtained from the methods providing microscopic and macroscopic characteristics of the system studied.     

Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation

The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostatic free energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, CCl4, and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.