Hydrophobic hydration at metal/water interfaces actively contributes to the energetics of electrochemical reactions, e.g. CO$_2$ and N$_2$ reduction, where small hydrophobic molecules are involved. In this work, constant applied potential molecular dynamics is employed to study hydrophobic hydration at a gold/water interface. We propose an extension of the Lum-Chandler-Weeks (LCW) theory to describe the free energy of hydrophobic hydration at the interface as a function of solute size and applied voltage. Based on this model we are able to predict the free energy cost of cavity formation at the interface directly from the free energy cost in the bulk plus an interface-dependent correction term. The interfacial water network contributes significantly to the free energy yielding a preference for outer-sphere adsorption at the gold surface for ideal hydrophobes. We predict an accumulation of small hydrophobic solutes of sizes comparable to CO or N$_2$, while the free energy cost to hydrate larger hydrophobes, above 2.5 Angstrom radius, is shown to be greater at the interface than in the bulk. Interestingly, the transition from the volume dominated to the surface dominated regimes predicted by the LCW theory in the bulk is also found to take place for hydrophobes at the Au/water interface, but occurs at smaller cavity radii. By applying the extended LCW theory to a simple model addition reaction, we illustrate some implications of our findings for electrochemical reactions.
An information theory model is used to construct a molecular explanation why hydrophobic solvation entropies measured in calorimetry of protein unfolding converge at a common temperature. The entropy convergence follows from the weak temperature dependence of occupancy fluctuations for molecular-scale volumes in water. The macroscopic expression of the contrasting entropic behavior between water and common organic solvents is the relative temperature insensitivity of the water isothermal compressibility. The information theory model provides a quantitative description of small molecule hydrati…
Hydrophobic hydration plays a crucial role in self-assembly processes over multiple length-scales, but the extrapolation of molecular-scale models to larger length-scale hydration phenomena is sometimes not warranted. Scaled-particle theories are based upon an interpolative view of that issue. We revisit the scaled-particle theory proposed thirty years ago by Stillinger, adopt a practical generalization, and consider the implications for hydrophobic hydration in light of our current understanding. The generalization is based upon identifying a molecular length, implicit in previous application…
An understanding of density fluctuations in bulk water has made significant contributions to our understanding of the hydration and interactions of idealized, purely repulsive hydrophobic solutes. To similarly inform the hydration of realistic hydrophobic solutes that have dispersive interactions with water, here we characterize water density fluctuations in the presence of attractive fields that correspond to solute-water attractions. We find that when the attractive field acts only in the solute hydration shell, but not in the solute core, it does not significantly alter water density fluctu…
Using a neural network potential (ANI-1ccx) generated from quantum data on a large data set of molecules and pairs of molecules, isothermal, constant volume simulations demonstrate that the model can be as accurate as ab initio molecular dynamics for simulations of pure liquid water and the aqueous solvation of a methane molecule. No theoretical or experimental data for the liquid phase is used to train the model, suggesting that the ANI-1ccx approach is an effective method to link high level ab initio methods to potentials for large scale simulations.
The strength of hydrogen bonding in water is stronger than that of van der waals interaction, therefore water may play an important role in the process of hydrophobic effects. When a hydrophobic solute is dissolved into water, an interface appears between the solute and water. To understand the mechanism of hydrophobic effects, it is necessary to study the structure of water and solute/water interface. In this study, based on the structural studies on water and air/water interface, the hydration free energy is derived, and utilized to investigate the physical origin of hydrophobic effects. Acc…
The thermodynamics of hydration changes gradually from entropic for small solutes to enthalpic for large ones. The small-to-large crossover lengthscale of hydrophobic hydration depends on the thermodynamic conditions of the solvent such as temperature, pressure, presence of additives, etc... We attempt to shed some light on the temperature dependence of the crossover lengthscale by using a probabilistic approach to water hydrogen bonding that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of both its distance to a solute and solute radius. …
In our recent works, based on the structural studies on water and interfacial water (topmost water layer at the solute/water interface), hydration free energy is derived and utilized to investigate the physical origin of hydrophobic interactions. In this study, it is extended to investigate the structural origin of hydration repulsive force. As a solute is embedded into water, it mainly affects the structure of interfacial water, which is dependent on the geometric shape of solute. Therefore, hydrophobic interactions may be related to the surface roughness of solute. According to this study, h…
AIMD results on a liquid krypton-water system are compared to recent XAFS results for the radial hydration structure for a Kr atom in liquid water solution. The comparisons with the liquid solution results are satisfactory and significantly different from the radial distributions extracted from the data on the solid clathrate hydrate phase. The calculations also produce the coordination number distribution that can be examined for metastable coordination structures suggesting possibilities for clathrate-like organization; none are seen in these results. Clathrate pictures of hydrophobic hydrat…
We use appropriately defined short ranged reference models of liquid water to clarify the different roles local hydrogen bonding, van der Waals attractions, and long ranged electrostatic interactions play in the solvation and association of apolar solutes in water. While local hydrogen bonding in- teractions dominate hydrophobic effects involving small solutes, longer ranged electrostatic and dis- persion interactions are found to be increasingly important in the description of interfacial structure around large solutes. The hydrogen bond network sets the solute length scale at which a crossov…
We present a probabilistic approach to water-water hydrogen bonding that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of both its distance to a hydrophobic particle and hydrophobe radius. This approach can be used in the density functional theory (DFT) and computer simulations to examine particle size effects on the hydration of particles and on their solvent-mediated interaction. For example, it allows one to explicitly identify a water hydrogen bond contribution to the external potential whereto a water molecule is subjected near a hydr…
The free energies to evacuate the first hydration shell around a solute and a cavity defined by the first hydration shell depend on the system size. This observation interpreted within the quasichemical theory shows that both the hydrophilic and the hydrophobic contributions to hydration depend on the system size, decreasing with increasing system size. Although the net hydration free energy benefits somewhat from the balancing of hydrophilic and hydrophobic contributions, a large system still appears necessary to describe the effect of the solvent on the macromolecule.
The hydration thermodynamics of the GXG tripeptide relative to the reference GGG is often used to define the conditional hydration contribution of X. This quantity or the hydration thermodynamics of a small molecule analog of the side-chain or some combination of such estimates, have anchored the interpretation of seminal experiments on protein stability and folding. We show that such procedures to model protein hydration have significant limitations. We study the conditional hydration thermodynamics of the isoleucine side-chain in an extended pentapeptide and in helical deca-peptides, using a…
Recent studies of the hydration of micro- and nanoscale solutes have demonstrated a strong {\it coupling} between hydrophobic, dispersion and electrostatic contributions, a fact not accounted for in current implicit solvent models. We present a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy with respect to a solvent volume exclusion function. The solvent accessible surface is output of our theory. Our method is illustrated with the hydration of alkane-assembled solutes on different length scales, and captures the strong sensitivity to the particular form …
A theoretical approach is developed to quantify hydrophobic hydration and interactions on a molecular scale, with the goal of gaining insight into the molecular origins of hydrophobic effects. The model is based on the fundamental relation between the probability for cavity formation in bulk water resulting from molecular-scale density fluctuations, and the hydration free energy of the simplest hydrophobic solute, a hard particle. This probability is estimated using an information theory (IT) approach, incorporating experimentally available properties of bulk water -- the density and radial di…
A high level polarizable force field is used to study the temperature dependence of hydrophobic hydration of small-sized molecules from computer simulations. Molecular dynamics (MD) simulations of liquid water at various temperatures form the basis of free energy perturbation calculations that consider the onset and growth of a repulsive sphere. This repulsive sphere acts as a model construct for the hydrophobic species. In the present study, an extension is pursued for seven independent target temperatures, ranging from close to the freezing point almost up to the boiling point of liquid wate…
The local hydration around tetrameric Hb in its T$_0$ and R$_4$ conformational substates is analyzed based on molecular dynamics simulations. Analysis of the local hydrophobicity (LH) for all residues at the $α_1 β_2$ and $α_2 β_1$ interfaces, responsible for the quaternary T$\rightarrow$R transition, which is encoded in the MWC model, as well as comparison with earlier computations of the solvent accessible surface area (SASA), makes clear that the two quantities measure different aspects of hydration. Local hydrophobicity quantifies the presence and structure of water molecules at the interf…
This letter considers several physical arguments about contributions to hydrophobic hydration of inert gases, constructs default models to test them within information theories, and gives information theory predictions using those default models with moment information drawn from simulation of liquid water. Tested physical features include: packing or steric effects, the role of attractive forces that lower the solvent pressure, and the roughly tetrahedral coordination of water molecules in liquid water. Packing effects (hard sphere default model) and packing effects plus attractive forces (Le…
Direct, all-atom calculations of the free energy of hydration of aqueous deca-alanine structures --- holistically including backbone and side-chain interactions together --- show that attractive interactions and the thermal expansion of the solvent explain the inverse temperature signatures that have been interpreted traditionally in favor of hydrophobic mechanisms for stabilizing the structure and function of soluble proteins.
As the beneficial effects of curcumin have often been reported to be limited to its small concentrations, we have undertaken a study to find the aggregation properties of curcumin in water by varying the number of monomers. Our molecular dynamics simulation results show that the equilibrated structure is always an aggregated state with remarkable structural rearrangements as we vary the number of curcumin monomers from 4 to 16 monomers. We find that curcumin monomers form clusters in a very definite pattern where they tend to aggregate both in parallel and anti-parallel orientation of the phen…
For a first principles understanding of macromolecular processes, a quantitative understanding of the underlying free energy landscape and in particular its entropy contribution is crucial. The stability of biomolecules, such as proteins, is governed by the hydrophobic effect, which arises from competing enthalpic and entropic contributions to the free energy of the solvent shell. While the statistical mechanics of liquids, as well as molecular dynamics simulations have provided much insight, solvation shell entropies remain notoriously difficult to calculate, especially when spatial resolutio…
The interactions of a protein, its phase behavior, and ultimately, its ability to function, are all influenced by the interactions between the protein and its hydration waters. Here we study proteins with a variety of sizes, shapes, chemistries, and biological functions, and characterize their interactions with their hydration waters using molecular simulation and enhanced sampling techniques. We find that akin to extended hydrophobic surfaces, proteins situate their hydration waters at the edge of a dewetting transition, making them susceptible to unfavorable perturbations. We also find that …
Based on our recent study on physical origin of hydrophobic effects, this is applied to investigate the dependence of hydrophobic interactions on the solute size. As two same hydrophobic solutes are dissolved into water, the hydration free energy is determined, and the critical radius (Rc) is calculated to be 3.2 Angstrom. With reference to the Rc, the dissolved behaviors can be divided into initial and hydrophobic solvation processes. These can be demonstrated by the molecular dynamics simulations on C60-C60 fullerenes in water, and CH4-CH4 molecules in water. In the association of C60 fuller…
Recent progress on molecular theories of hydration of nonpolar solutes in aqueous solution has led to new ways of thinking about the old issue of free, or "available," volume in liquids. This article surveys the principal new results with particular attention to general issues of packing in liquids.
The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular density functional theory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third …
The solvation of carbon monoxide (CO) in liquid water is important for understanding its toxicological effects and biochemical roles. In this paper, we use ab initio molecular dynamics (AIMD) and CCSD(T)-F12 calculations to assess the accuracy of the Straub and Karplus molecular mechanical (MM) model for CO(aq). The CCSD(T)-F12 CO--H2O potential energy surfaces show that the most stable structure corresponds to water donating a hydrogen bond to the C center. The MM-calculated surface it incorrectly predicts that the O atom is a stronger hydrogen bond acceptor than the C atom. The AIMD simulati…
Molecular dynamics simulations have revealed a dramatic increase, with increasing temperature, of the amplitude of electrostatic fluctuations caused by water at the active site of metalloprotein plastocyanin. The increased breadth of electrostatic fluctuations, expressed in terms of the reorganization energy of changing the redox state of the protein, is related to the formation of the hydrophobic protein/water interface allowing large-amplitude collective fluctuations of the water density in the protein's first solvation shell. On the top of the monotonic increase of the reorganization energy…
We investigate the impact of water fluctuations on the key-lock association kinetics of a hydrophobic ligand (key) binding to a hydrophobic pocket (lock) by means of a minimalistic stochastic model system. It describes the collective hydration behavior of the pocket by bimodal fluctuations of a water-pocket interface that dynamically couples to the diffusive motion of the approaching ligand via the hydrophobic interaction. This leads to a set of overdamped Langevin equations in 2D-coordinate-space, that is Markovian in each dimension. Numerical simulations demonstrate locally increased frictio…
Hydration of hydrophobic solutes in water is the cause of different phenomena, including the hydrophobic heat-capacity anomaly, which are not yet fully understood. Because of its topicality, there has recently been growing interest in the mechanism of hydrophobic aggregation, and in the physics on which it is based. In this study we use a simple yet powerful mixture model for water, an adapted two-state Muller-Lee-Graziano model, to describe the energy levels of water molecules as a function of their proximity to non-polar solute molecules. The model is shown to provide an appropriate descript…
Water offers a large temperature domain of stable liquid, and the characteristic hydrophobic effects are first a consequence of the temperature insensitivity of equation-of-state features of the aqueous medium, compared to other liquids. On this basis, the known aqueous media and conditions offer low risk compared to alternatives as a matrix to which familiar molecular biological structures and processes have adapted. The current molecular-scale understanding of hydrophobic hydration is not conformant in detail with a standard structural entropy rationalization. That classic pictorial explanat…
Simulations show Gly$_{15}$, a polypeptide lacking any side-chains, can collapse in water. We assess the hydration thermodynamics in this collapse by calculating the hydration free energy at each of the end points of the reaction coordinate, here the end-to-end distance ($r$) in the chain. To examine the role of the various conformations for a given $r$, we study the conditional distribution, $P(R_g | r)$, of the radius of gyration for a given value of $r$. $P(R_g|r)$ is found to vary more gently compared to the corresponding variation in the excess hydration free energy. Using this insight wi…
The small r variation of the probability density P(r) for end-to-end separations of a -CH2CH3 capped (-OCH2CH2-)n oligomer in water is computed to be closely similar to the CH4 ... CH4 potential of mean force under the same circumstances. Since the aqueous solution CH4 ... CH4 potential of mean force is the natural physical definition of a primitive hydrophobic bond, the present result identifies an experimentally accessible circumstance for direct observation of a hydrophobic bond which has not been observed previously because of the low solubility of CH4 in water. The physical picture is tha…
We study, by Monte Carlo simulations, a coarse-grained model of a water monolayer between hydrophobic walls at partial hydration, with a wall-to-wall distance of about 0.5 nm. We analyze how the diffusion constant parallel to the walls, $D_{\parallel}$, changes and correlates to the phase diagram of the system. We find a locus of $D_{\parallel}$ maxima and a locus of $D_{\parallel}$ minima along isotherms, with lines of constant $D_{\parallel}$ resembling the melting line of bulk water. The two loci of $D_{\parallel}$ extrema envelope the line of temperatures of density maxima at constant $P$.…
The unique physical and optical properties of nanoparticles make their reliable and rapid assembly an important goal for nanotechnology. To this end, many competing driving forces have been targeted to control the self-assembly, though issues with reliability and efficiency indicate that interfaces on the nanoscale are not yet fully understood. In this letter we report for the first time that the flow of water media from the interface between chemically nanopatterned hydrophobic surfaces and adjacent hydrophilic regions (a Janus interface) can effectively be employed for rapid nanoparticle ass…
It is known that steric blocking by peptide sidechains of hydrogen bonding, HB, between water and peptide groups, PGs, in beta sheets accords with an amino acid intrinsic beta sheet preference. The present observations with Quantum Molecular Dynamics, QMD, simulation with quantum mechanical treatment of every water molecule solvating a beta sheet that would be transient in nature suggest that this steric blocking is not applicable in a hydrophobic region unless a cation is present, so that the amino acid beta sheet preference due to this steric blocking is only effective in the presence of a c…
Dipolar susceptibility of interfacial water and the corresponding interface dielectric constant were calculated from numerical molecular dynamics simulations for neutral and charged states of buckminsterfullerene C$_{60}$. Dielectric constants in the range 10--22, depending on temperature and solute charge, were found. The hydration water undergoes a structural crossover as a function of the solute charge. Its main signatures include the release of dangling O-H bonds pointing toward the solute and the change in the preferential orientations of hydration water from those characterizing hydropho…
We perform systematic molecular dynamics simulations of water confined between two nanoscale plates at T=300 K. We investigate the effect of pressure (-0.15 GPa <= P <= 0.2 GPa) and plate separation (0.4 nm <= d <= 1.6 nm) on the phase behavior of water when the plates are either hydrophobic or hydrophilic. When water is confined between hydrophobic plates, capillary evaporation occurs between the plates at low enough P. The threshold value of d at which this transition occurs decreases with P (e.g., 1.6 nm at P ~ -0.05 GPa; 0.5 nm at P \~ 0.1 GPa), until, at high P, no capillary evaporation o…
Motivated by recent experiments showing the promise of noble gases as cryoprotectants, we perform molecular dynamics modeling of phase transitions in water with xenon under cooling. We study the structure and dynamics of xenon water solution as a function of temperature. Homogeneous nucleation of clathrate hydrate phase is observed and characterized. As the temperature is further reduced we observe hints of dissociation of clathrate due to stronger hydrophobic hydration, pointing towards a possible instability of clathrate at cryogenic temperatures and conversion to an amorphous phase comprise…
We address the problem of predicting the solvation free energy and equilibrium solvent density profile in fews minutes from the molecular density functional theory beyond the usual hypernetted-chain approximation. We introduce a bridge functional of a coarse-grained, weighted solvent density. In few minutes at most, for solutes of sizes ranging from small compounds to large proteins, we produce (i) an estimation of the free energy of solvation within 1 kcal/mol of the experimental data for the hydrophobic solutes presented here, and (ii) the solvent distribution around the solute. Contrary to …
The water dynamics, as characterized by the local hydrophobicity (LH), is investigated for tetrameric hemoglobin and dimeric melittin. For the T0 to R0 transition in Hb it is found that LH provides additional molecular-level insight into the Perutz mechanism, i.e., the breaking and formation of salt bridges at the alpha1 / beta2 and alpha2 / beta1 interface is accompanied by changes in LH. For Hb in cubic water boxes with 90 Aengstroem and 120 Aengstroem edge length it is observed that following a decrease in LH as a consequence of reduced water density or change of water orientation at the pr…
