An information theory model of hydrophobic interactions

Putting water on a lattice: the importance of long wavelength density fluctuations in theories of hydrophobic and interfacial phenomena

The physics of air-water interfaces plays a central role in modern theories of the hydrophobic effect. Implementing these theories, however, has been hampered by the difficulty of addressing fluctuations in the shape of such soft interfaces. We show that this challenge is a fundamental consequence of mapping long wavelength density variations onto discrete degrees of freedom. Drawing from studies of surface roughness in lattice models, we account for the resulting nonlinearities simply but accurately. Simulations show that this approach captures complex solvation behaviors quantitatively.

Sensitivity of local hydration behaviour and conformational preferences of peptides to choice of water model

Secondary structural preferences of the beta-hairpin of the 2GB1 protein in the folded and unfolded ensembles are shown to be sensitive to the choice of water model.

Field-SEA: a model for computing the solvation free energies of nonpolar, polar, and charged solutes in water

Previous work describes a computational solvation model called semi-explicit assembly (SEA). The SEA water model computes the free energies of solvation of nonpolar and polar solutes in water with good efficiency and accuracy. However, SEA gives systematic errors in the solvation free energies of ions and charged solutes. Here, we describe field-SEA, an improved treatment that gives accurate solvation free energies of charged solutes, including monatomic and polyatomic ions and model dipeptides, as well as nonpolar and polar molecules. Field-SEA is computationally inexpensive for a given solute because explicit-solvent model simulations are relegated to a precomputation step and because it represents solvating waters in terms of a solute’s free-energy field. In essence, field-SEA approximates the physics of explicit-model simulations within a computationally efficient framework. A key finding is that an atom’s solvation shell inherits characteristics of a neighboring atom, especially strongly charged neighbors. Field-SEA may be useful where there is a need for solvation free-energy computations that are faster than explicit-solvent simulations and more accurate than traditional implicit-solvent simulations for a wide range of solutes.

Molecular-scale hydrophobic interactions between hard-sphere reference solutes are attractive and endothermic

The osmotic second virial coefficients, B2, for atomic-sized hard spheres in water are attractive (B2 < 0) and become more attractive with increasing temperature (ΔB2/ΔT < 0) in the temperature range 300 K ≤ T ≤ 360 K. Thus, these hydrophobic interactions are attractive and endothermic at moderate temperatures. Hydrophobic interactions between atomic-sized hard spheres in water are more attractive than predicted by the available statistical mechanical theory. These results constitute an initial step toward detailed molecular theory of additional intermolecular interaction features, specifically, attractive interactions associated with hydrophobic solutes.

Soft collective fluctuations governing hydrophobic association

The interaction between two associating hydrophobic particles has traditionally been explained in terms of the release of entropically frustrated hydration shell water molecules. However, this picture cannot account for the kinetics of hydrophobic association and is therefore not capable of providing a microscopic description of the hydrophobic interaction (HI). Here, Monte Carlo simulations of a pair of molecular-scale apolar solutes in aqueous solution reveal the critical role of collective fluctuations in the hydrogen bond (HB) network for the microscopic picture of the HI. The main contribution to the HI is the relaxation of solute-water translational correlations. The existence of a heat capacity maximum at the desolvation barrier is shown to arise from softening of non-HB water fluctuations and the relaxation of many-body correlations in the labile HB network. The microscopic event governing the kinetics of hydrophobic association has turned out to be a relatively large critical collective fluctuation in hydration water displacing a substantial fraction of HB clusters from the inner to the outer region of the first hydration shell.

Water and water-like liquids: relationships between structure, entropy and mobility

Liquids with very diverse underlying interactions share the thermodynamic and transport anomalies of water, including metalloids, ionic melts and mesoscopic fluids. The generic feature that characterises such water-like liquids is a density-driven shift in the nature of local order in the condensed phases. The key semiquantitative relationships between structural order, thermodynamics and transport that are necessary in order to map out the consequences of this common qualitative feature for liquid-state properties and phase transformations of such systems are reviewed here. The application of these ideas to understand and model tetrahedral liquids, especially water, is discussed and possible extensions to other complex fluids are considered.

Hydration of metal surfaces can be dynamically heterogeneous and hydrophobic

We have applied molecular dynamics and methods of importance sampling to study structure and dynamics of liquid water in contact with metal surfaces. The specific surfaces considered resemble the 100 and 111 faces of platinum. Several results emerge that should apply generally, not just to platinum. These results are generic consequences of water molecules binding strongly to surfaces that are incommensurate with favorable hydrogen-bonding patterns. We show that adlayers of water under these conditions have frustrated structures that interact unfavorably with adjacent liquid water. We elucidate dynamical processes of water in these cases that extend over a broad range of timescales, from less than picoseconds to more than nanoseconds. Associated spatial correlations extend over nanometers. We show that adlayer reorganization occurs intermittently, and each reorganization event correlates motions of several molecules. We show that soft liquid interfaces form adjacent to the adlayer, as is generally characteristic of liquid water adjacent to a hydrophobic surface. The infrequent adlayer reorganization produces a hydrophobic heterogeneity that we characterize by studying the degrees by which different regions of the adlayers attract small hydrophobic particles. Consequences for electrochemistry are discussed in the context of hydronium ions being attracted from the liquid to the metal–adlayer surface.

Anionic and cationic Hofmeister effects on hydrophobic and hydrophilic surfaces

Using a two-step modeling approach, we address the full spectrum of direct, reversed, and altered ionic sequences as the charge of the ion, the charge of the surface, and the surface polarity are varied. From solvent-explicit molecular dynamics simulations, we extract single-ion surface interaction potentials for halide and alkali ions at hydrophilic and hydrophobic surfaces. These are used within Poisson-Boltzmann theory to calculate ion density and electrostatic potential distributions at mixed polar/unpolar surfaces for varying surface charge. The resulting interfacial tension increments agree quantitatively with experimental data and capture the Hofmeister series, especially the anomaly of lithium, which is difficult to obtain using continuum theory. Phase diagrams that feature different Hofmeister series as a function of surface charge, salt concentration, and surface polarity are constructed from the long-range force between two surfaces interacting across electrolyte solutions. Large anions such as iodide have a high hydrophobic surface affinity and increase the effective charge magnitude on negatively charged unpolar surfaces. Large cations such as cesium also have a large hydrophobic surface affinity and thereby compensate an external negative charge surface charge most efficiently, which explains the well-known asymmetry between cations and anions. On the hydrophilic surface, the size-dependence of the ion surface affinity is reversed, explaining the Hofmeister series reversal when comparing hydrophobic with hydrophilic surfaces.

The Influence of Water on the Solubility of Carbon Dioxide in Imidazolium Based Ionic Liquids

We explore the influence of small amounts of water dissolved in 1-alkyl-3-methyl-imidazolium based ionic liquids (ILs) on the solubility of CO2 as a function of water content and temperature. We observe a decreasing solubility of CO2 as function of increasing water content in almost quantitative agreement with recent experimental data by Husson et al. [Fluid Phase Eq. 294, 98 (2010)]. In addition, a purely repulsive variant of CO2 is employed as a test-case to elucidate the solvation behavior of small sized molecules in absence of favorable interactions. We find that the decreasing solubility is about one third due to the increasing solvent number density, and about two thirds due to the change in solvation free energy. In addition, we observe that the computed solvation free energy of a purely repulsive test-molecule increases even more strongly with increasing water content, indicating that small favorable “interaction sites” within the liquid, well suited for accommodating a CO2 molecule, become increasingly rare due to the competition with the water molecules.

Water interfaces, solvation, and spectroscopy

Liquid water consistently expands our appreciation of the rich statistical mechanics that can emerge from simple molecular constituents. Here I review several interrelated areas of recent work on aqueous systems that aim to explore and explain this richness by revealing molecular arrangements, their thermodynamic origins, and the timescales on which they change. Vibrational spectroscopy of OH stretching features prominently in these discussions, with an emphasis on efforts to establish connections between spectroscopic signals and statistics of intermolecular structure. For bulk solutions, the results of these efforts largely verify and enrich existing physical pictures of hydrogen-bond network connectivity, dynamics, and response. For water at interfaces, such pictures are still emerging. As an important example I discuss the solvation of small ions at the air-water interface, whose surface propensities challenge a basic understanding of how aqueous fluctuations accommodate solutes in heterogeneous environments.

Single polymer studies of hydrophobic hydration

Hydrophobic interactions guide protein folding, multidomain protein assembly, receptor-ligand binding, membrane formation, and cellular transportation. On the macroscale, hydrophobic interactions consist of the aggregation of "oil-like" objects in water by minimizing the interfacial energy. However, studies of the hydration behavior of small hydrophobic molecules have shown that the microscopic (~1 nm) hydration mechanism differs fundamentally from its macroscopic counterpart. Theoretical studies over the last two decades have pointed to an intricate dependence of molecular hydration mechanisms on the length scale. The microscopic-to-macroscopic crossover length scale is critically important to hydrophobic interactions in polymers, proteins, and other macromolecules. Accurate experimental determination of hydration mechanisms and interaction strengths directly influence our understanding of protein folding. In this Account, we discuss our recent measurements of the hydration energies of single hydrophobic homopolymers as they unfold. We describe in detail our single molecule force spectroscopy technique, the interpretation of the single polymer force curve, and how it relates to the hydration free energy of a hydrophobic polymer. Specifically, we show how temperature, side-chain sizes and solvent conditions, affect the driving force of hydrophobic collapse. The experiments reveal that the size of the nonpolar polymer side-chains changes the thermal signatures of hydration. The sizes of the polymer side-chains bridge the length scale where theories had predicted a transition between entropically driven microscopic hydration and enthalpically driven macroscopic hydrophobic hydration. Our experimental results revealed a crossover length scale of approximately 1 nm, similar to the results from recent theoretical studies. Experiments that probe solvent dependency show that the microscopic polymer hydration is correlated with macroscopic interfacial tension. Consistent with theoretical predictions, the solvent conditions affect the microscopic and macroscopic hydrophobic strengths in similar ways. Although the extended polymers and proteins span hundreds of nanometers, the experiments show that their hydration behavior is determined by the size of a single hydrophobic monomer. As the hydrophobic particle size decreases from the macroscopic to the microscopic regime, the scaling relationship changes from a dependence on interfacial area to a dependence on volume. Therefore, under these conditions, the driving force for the aggregation of hydrophobic molecules is reduced, which has significant implications for the strength of hydrophobic interactions in molecular systems, particularly in protein folding.

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

Physical origin underlying the entropy loss upon hydrophobic hydration

The hydrophobic effect (HE) is commonly associated with the demixing of oil and water at ambient conditions and plays the leading role in determining the structure and stability of biomolecular assembly in aqueous solutions. On the molecular scale HE has an entropic origin. It is believed that hydrophobic particles induce order in the surrounding water by reducing the volume of configuration space available for hydrogen bonding. Here we show with computer simulation results that this traditional picture, based on average structural features of hydration water, configurational properties of single water molecules, and up to pairwise correlations, is not correct. Analyzing collective fluctuations in water clusters we are able to provide a fundamentally new picture of HE based on pronounced many-body correlations affecting the switching of hydrogen bonds (HBs) between molecules. These correlations emerge as a nonlocal compensation of reduced fluctuations of local electrostatic fields in the presence of an apolar solute. We propose an alternative view which may also be formulated as a maximization principle: The electrostatic noise acting on water molecules is maximized under the constraint that each water molecule on average maintains as many HBs as possible. In the presence of the solute the maximized electrostatic noise is a result of nonlocal fluctuations in the labile HB network giving rise to strong correlations among at least up to four water molecules.

Hydration and anomalous solubility of the Bell-Lavis model as solvent

We address the investigation of the solvation properties of the minimal orientational model for water originally proposed by [Bell and Lavis, J. Phys. A 3, 568 (1970)]. The model presents two liquid phases separated by a critical line. The difference between the two phases is the presence of structure in the liquid of lower density, described through the orientational order of particles. We have considered the effect of a small concentration of inert solute on the solvent thermodynamic phases. Solute stabilizes the structure of solvent by the organization of solvent particles around solute particles at low temperatures. Thus, even at very high densities, the solution presents clusters of structured water particles surrounding solute inert particles, in a region in which pure solvent would be free of structure. Solute intercalates with solvent, a feature which has been suggested by experimental and atomistic simulation data. Examination of solute solubility has yielded a minimum in that property, which may be associated with the minimum found for noble gases. We have obtained a line of minimum solubility (TmS) across the phase diagram, accompanying the line of maximum density. This coincidence is easily explained for noninteracting solute and it is in agreement with earlier results in the literature. We give a simple argument which suggests that interacting solute would dislocate TmS to higher temperatures.

Kinetics of bulge bases in small RNAs and the effect of pressure on it

Due to their self-catalytic properties, small RNAs with bulge bases are hypothesized to be primordial molecules which could form elementary translation systems. Using molecular dynamics simulations, we study the binding propensity of small RNAs by calculating the free energy barrier corresponding to the looped out conformations of bulge bases, which presumably act as the binding sites for ligands in these small RNAs. We find that base flipping kinetics can proceed at atmospheric pressure but with a very small propensity. Furthermore, the free energy barrier associated with base flipping depends on the stacking with neighboring bases. Next, we studied the base flipping kinetics with pressure. We find that the free energy associated with base looping out increases monotonically as the pressure is increased. Furthermore, we calculate the mean first-passage time of conformational looping out of the bulge base using the diffusion of reaction coordinate associated with the base flipping on the underlying free energy surface. We find that the mean first-passage time associated with bulge looping out increases slowly upon increasing pressures up to atm but changes dramatically for atm. Finally, we discuss our results in the light of the role of hydration shell of water around RNA. Our results are relevant for the RNA world hypothesis.

Structure and anomalous solubility for hard spheres in an associating lattice gas model

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture.

Temperature dependence of water interactions with the amide carbonyls of α-helices

Hydration is a key determinant of the folding, dynamics, and function of proteins. In this study, temperature-dependent Fourier transform infrared (FTIR) spectroscopy combined with singular value decomposition (SVD) and global fitting were used to investigate both the interaction of water with α-helical proteins and the cooperative thermal unfolding of these proteins. This methodology has been applied to an isolated α-helix (Fs peptide) and to globular α-helical proteins including the helical subdomain and full-length villin headpiece (HP36 and HP67). The results suggest a unique IR signature for the interaction of water with the helical amide carbonyl groups of the peptide backbone. The IR spectra indicate a weakening of the net hydrogen bond strength of water to the backbone carbonyls with increasing temperature. This weakening of the backbone solvation occurs as a discrete transition near the maximum of the temperature-dependent hydrophobic effect, not a continuous change with increasing temperature. Possible molecular origins of this effect are discussed with respect to previous molecular dynamics simulations of the temperature-dependent solvation of the helix backbone.

Analytical model for three-dimensional Mercedes-Benz water molecules

We developed a statistical model which describes the thermal and volumetric properties of water-like molecules. A molecule is presented as a three-dimensional sphere with four hydrogen-bonding arms. Each water molecule interacts with its neighboring waters through a van der Waals interaction and an orientation-dependent hydrogen-bonding interaction. This model, which is largely analytical, is a variant of a model developed before for a two-dimensional Mercedes-Benz model of water. We explored properties such as molar volume, density, heat capacity, thermal expansion coefficient, and isothermal compressibility as a function of temperature and pressure. We found that the volumetric and thermal properties follow the same trends with temperature as in real water and are in good general agreement with Monte Carlo simulations, including the density anomaly, the minimum in the isothermal compressibility, and the decreased number of hydrogen bonds upon increasing the temperature.

Simple model of hydrophobic hydration

Water is an unusual liquid in its solvation properties. Here, we model the process of transferring a nonpolar solute into water. Our goal was to capture the physical balance between water's hydrogen bonding and van der Waals interactions in a model that is simple enough to be nearly analytical and not heavily computational. We develop a 2-dimensional Mercedes-Benz-like model of water with which we compute the free energy, enthalpy, entropy, and the heat capacity of transfer as a function of temperature, pressure, and solute size. As validation, we find that this model gives the same trends as Monte Carlo simulations of the underlying 2D model and gives qualitative agreement with experiments. The advantages of this model are that it gives simple insights and that computational time is negligible. It may provide a useful starting point for developing more efficient and more realistic 3D models of aqueous solvation.

Predicting cavity formation free energy: how far is the Gaussian approximation valid?

We examine the range of validity of the Gaussian model for various water-like liquids whose intermolecular potentials differ from SPC/E water, to provide insight into the temperature dependence of the hydrophobic effect for small hard sphere solutes. We find that low compressibility liquids that have more close-packed network structures show much larger deviations from Gaussian fluctuations for low or zero occupancies relative to more compressible fluids with more open networks. Water appears to be a unique molecular fluid in possessing equilibrium density fluctuations that are faithfully described by the Gaussian theory. We ascribe this success to the fact, shown here, that the orientational correlations near a small hard sphere solute involve remarkably little reorganization from the bulk, which is a consequence of water's low solvent reorganization enthalpy and entropy.

Hydrophobicity of proteins and interfaces: insights from density fluctuations

Macroscopic characterizations of hydrophobicity (e.g., contact angle measurements) do not extend to the surfaces of proteins and nanoparticles. Molecular measures of hydrophobicity of such surfaces need to account for the behavior of hydration water. Theory and state-of-the-art simulations suggest that water density fluctuations provide such a measure; fluctuations are enhanced near hydrophobic surfaces and quenched with increasing surface hydrophilicity. Fluctuations affect conformational equilibria and dynamics of molecules at interfaces. Enhanced fluctuations are reflected in enhanced cavity formation, more favorable binding of hydrophobic solutes, increased compressibility of hydration water, and enhanced water-water correlations at hydrophobic surfaces. These density fluctuation-based measures can be used to develop practical methods to map the hydrophobicity/philicity of heterogeneous surfaces including those of proteins. They highlight that the hydrophobicity of a group is context dependent and is significantly affected by its environment (e.g., chemistry and topography) and especially by confinement. The ability to include information about hydration water in mapping hydrophobicity is expected to significantly impact our understanding of protein-protein interactions as well as improve drug design and discovery methods and bioseparation processes.

Hydrophobic drying and hysteresis at different length scales by molecular dynamics simulations

We performed molecular dynamics simulations to investigate hydrophobic interactions between two parallel hydrophobic plates immersed in water. The two plates are separated by a distance D ranging from contact to a few nanometers. To mimic the attractive hydrophobic force measurement in a surface force experiment, a driving spring is used to measure the hydrophobic force between two hydrophobic plates. The force-distance curves, in particular the force variations from spontaneous drying to hydrophobic collapse are obtained. These details are usually not accessible in the surface force measurement due to the unstable jump into contact. The length-scale effect on the hydrophobic drying during normal approach and the hydrophobic hysteresis during retraction has been studied. We find that the critical distance at which a spontaneous drying occurs is determined by the shorter characteristic dimension of the plate, whereas the hydrophobic hysteresis is determined by the longer characteristic dimension of the plate. The variations of the potential of mean force versus separation during approach and retraction are also calculated. The results show that water confined between two parallel hydrophobic plates is in a thermodynamic metastable state. This comparably high energy state leads to the spontaneous drying at some critical distance.

Confinement induced conformational changes in n-alkanes sequestered within a narrow carbon nanotube

While alkanes in solution exhibit predominantly extended conformations, nanoscale confinement of these chains within protein binding sites and synthetic receptors can significantly alter the conformer distribution. As a simple model for the effect of confinement on the conformation, we report molecular simulations of n-alkanes absorbed from a bulk solvent into narrow carbon nanotubes. We observe that confinement of butane, hexane, and tetracosane induces a trans to gauche conformational redistribution. Moreover, confined hexane and tetracosane exhibit cooperative interactions between neighboring dihedral angles, which promote a helical gauche conformation for the portions of the chain within the nanotube. Hexane absorbed into the nanotube from water or benzene exhibits essentially the same conformation regardless of the bulk solvent. The PMF between the nanotube and hexane along the central nanotube axis finds that nanotube absorption is favorable from aqueous solution but neutral from benzene. The interaction between hexane and the nanotube in water is dominated by the direct interaction between the alkane and the nanotube and weakly opposed by indirect water-mediated forces. In benzene, however, the direct alkane/nanotube interaction is effectively balanced by the indirect benzene-mediated interaction. Our simulations in water stand in difference to standard interpretations of the hydrophobic effect, which posit that the attraction between non-polar species in water is driven by their mutual insolubility.

Geofold: topology-based protein unfolding pathways capture the effects of engineered disulfides on kinetic stability

Protein unfolding is modeled as an ensemble of pathways, where each step in each pathway is the addition of one topologically possible conformational degree of freedom. Starting with a known protein structure, GeoFold hierarchically partitions (cuts) the native structure into substructures using revolute joints and translations. The energy of each cut and its activation barrier are calculated using buried solvent accessible surface area, side chain entropy, hydrogen bonding, buried cavities, and backbone degrees of freedom. A directed acyclic graph is constructed from the cuts, representing a network of simultaneous equilibria. Finite difference simulations on this graph simulate native unfolding pathways. Experimentally observed changes in the unfolding rates for disulfide mutants of barnase, T4 lysozyme, dihydrofolate reductase, and factor for inversion stimulation were qualitatively reproduced in these simulations. Detailed unfolding pathways for each case explain the effects of changes in the chain topology on the folding energy landscape. GeoFold is a useful tool for the inference of the effects of disulfide engineering on the energy landscape of protein unfolding.

Water-exclusion and liquid-structure forces in implicit solvation

A continuum model of solvation is proposed to describe (i) long-range electrostatic effects of water exclusion resulting from incomplete and anisotropic hydration in crowded environments and (ii) short-range effects of liquid-structure forces on the hydrogen-bond interactions at solute/water interfaces. The model is an extension of the phenomenological screened coulomb potential-based implicit model of solvation. The developments reported here allow a more realistic representation of highly crowded and spatially heterogeneous environments, such as those in the interior of a living cell. Only the solvent is treated as a continuum medium. It is shown that the electrostatic effects of long-range water-exclusion can strongly affect protein-protein binding energies and are then related to the thermodynamics of complex formation. Hydrogen-bond interactions modulated by the liquid structure at interfaces are calibrated based on systematic calculations of potentials of mean force in explicit water. The electrostatic component of the model is parametrized for monovalent, divalent and trivalent ions. The conceptual and practical aspects of the model are discussed based on simulations of protein complexation and peptide folding. The current implementation is ~1.5 times slower than the gas-phase force field and exhibits good parallel performance.

Extended surfaces modulate hydrophobic interactions of neighboring solutes

Interfaces are a most common motif in complex systems. To understand how the presence of interfaces affects hydrophobic phenomena, we use molecular simulations and theory to study hydration of solutes at interfaces. The solutes range in size from subnanometer to a few nanometers. The interfaces are self-assembled monolayers with a range of chemistries, from hydrophilic to hydrophobic. We show that the driving force for assembly in the vicinity of a hydrophobic surface is weaker than that in bulk water and decreases with increasing temperature, in contrast to that in the bulk. We explain these distinct features in terms of an interplay between interfacial fluctuations and excluded volume effects--the physics encoded in Lum-Chandler-Weeks theory [Lum K, Chandler D, Weeks JD (1999) J Phys Chem B 103:4570-4577]. Our results suggest a catalytic role for hydrophobic interfaces in the unfolding of proteins, for example, in the interior of chaperonins and in amyloid formation.

Quantifying density fluctuations in volumes of all shapes and sizes using indirect umbrella sampling

Water density fluctuations are an important statistical mechanical observable that is related to many-body correlations, as well as hydrophobic hydration and interactions. Local water density fluctuations at a solid-water surface have also been proposed as a measure of it's hydrophobicity. These fluctuations can be quantified by calculating the probability, P(v)(N), of observing N waters in a probe volume of interest v. When v is large, calculating P(v)(N) using molecular dynamics simulations is challenging, as the probability of observing very few waters is exponentially small, and the standard procedure for overcoming this problem (umbrella sampling in N) leads to undesirable impulsive forces. Patel et al. [J. Phys. Chem. B, 114, 1632 (2010)] have recently developed an indirect umbrella sampling (INDUS) method, that samples a coarse-grained particle number to obtain P(v)(N) in cuboidal volumes. Here, we present and demonstrate an extension of that approach to volumes of other basic shapes, like spheres and cylinders, as well as to collections of such volumes. We further describe the implementation of INDUS in the NPT ensemble and calculate P(v)(N) distributions over a broad range of pressures. Our method may be of particular interest in characterizing the hydrophobicity of interfaces of proteins, nanotubes and related systems.

Physical Modeling of Aqueous Solvation

We consider the free energies of solvating molecules in water. Computational modeling usually involves either detailed explicit-solvent simulations, or faster computations, which are based on implicit continuum approximations or additivity assumptions. These simpler approaches often miss microscopic physical details and non-additivities present in experimental data. We review explicit-solvent modeling that identifies the physical bases for the errors in the simpler approaches. One problem is that water molecules that are shared between two substituent groups often behave differently than waters around each substituent individually. One manifestation of non-additivities is that solvation free energies in water can depend not only on surface area or volume, but on other properties, such as the surface curvature. We also describe a new computational approach, called Semi-Explicit Assembly, that aims to repair these flaws and capture more of the physics of explicit water models, but with computational efficiencies approaching those of implicit-solvent models.

Comparison of Tetrahedral Order, Liquid State Anomalies, and Hydration Behavior of mTIP3P and TIP4P Water Models

The relationship between local tetrahedral order, tagged particle potential energy, and coordination number is studied for mTIP3P and TIP4P models of water in the bulk as well as in the neighborhood of a small peptide. The tendency of water molecules with different binding or tagged particle potential energies to occupy environments with different degrees of disorder can be effectively illustrated by constructing tetrahedral order distributions and corresponding entropy metrics conditional on restricted ranges of local binding energy. At the state point corresponding to the onset of the density anomaly, the correlation between tetrahedral entropy versus tagged potential energy is strong and virtually identical for mTIP3P and TIP4P. In TIP4P, this correlation is retained up to temperatures as high as 300 K, while it is lost by 250 K in mTIP3P. In the 250-300 K regime that is important for biomolecular simulations, mTIP3P behaves essentially as a simple liquid while TIP4P shows the density and related anomalies characteristic of water. We also study the number of water molecules, the tetrahedral order, and the tagged molecule potential energies for water molecules as a function of the distance from the peptide for the 16-residue β-hairpin fragment of 2GB1 in mTIP3P and TIP4P solvents. The hydration shell coordination profiles (n(r)) of the number of water molecules are almost identical in the two solvents, but the radial variation in the local energies and local order show significant differences. The residue-wise variation in the tagged potential energy of water molecules within the first hydration shell is qualitatively similar in the two models. A comparison of the tetrahedral order distributions of water molecules lying at different distances from the biomolecular solute shows that the perturbation in the local tetrahedral order distributions of the bulk solvent due to the presence of the solute is marginal. Thus, in the 250-300 K regime, the mTIP3P and TIP4P water models show qualitatively different behavior in terms of the relationship between tetrahedral order and local energy, but as solvents in the neighborhood of a biomolecular solute, the differences between the two models are only quantitative and not qualitative.

Signature of hydrophobic hydration in a single polymer

Hydrophobicity underpins self-assembly in many natural and synthetic molecular and nanoscale systems. A signature of hydrophobicity is its temperature dependence. The first experimental evaluation of the temperature and size dependence of hydration free energy in a single hydrophobic polymer is reported, which tests key assumptions in models of hydrophobic interactions in protein folding. Herein, the hydration free energy required to extend three hydrophobic polymers with differently sized aromatic side chains was directly measured by single molecule force spectroscopy. The results are threefold. First, the hydration free energy per monomer is found to be strongly dependent on temperature and does not follow interfacial thermodynamics. Second, the temperature dependence profiles are distinct among the three hydrophobic polymers as a result of a hydrophobic size effect at the subnanometer scale. Third, the hydration free energy of a monomer on a macromolecule is different from a free monomer; corrections for the reduced hydration free energy due to hydrophobic interaction from neighboring units are required.

Hydrophobic interactions increase attachment of gum Arabic- and PVP-coated Ag nanoparticles to hydrophobic surfaces

A fundamental understanding of attachment of surface-coated nanoparticles (NPs) is essential to predict the distribution and potential risks of NPs in the environment. Column deposition studies were used to examine the effect of surface-coating hydrophobicity on NP attachment to collector surfaces in mixtures with varying ratios of octadecylichlorosilane (OTS)-coated (hydrophobic) glass beads and clean silica (hydrophilic) glass beads. Silver nanoparticles (AgNPs) coated with organic coatings of varying hydrophobicity, including citrate, polyvinylpyrrolidone (PVP), and gum arabic (GA), were used. The attachment efficiencies of GA and PVP AgNPs increased by 2- and 4-fold, respectively, for OTS-coated glass beads compared to clean glass beads. Citrate AgNPs showed no substantial change in attachment efficiency for hydrophobic compared to hydrophilic surfaces. The attachment efficiency of PVP-, GA-, and citrate-coated AgNPs to hydrophobic collector surfaces correlated with the relative hydrophobicity of the coatings. The differences in the observed attachment efficiencies among AgNPs could not be explained by classical DLVO, suggesting that hydrophobic interactions between AgNPs and OTS-coated glass beads were responsible for the increase in attachment of surface-coated AgNPs with greater hydrophobicity. This study indicates that the overall attachment efficiency of AgNPs will be influenced by the hydrophobicity of the NP coating and the fraction of hydrophobic surfaces in the environment.