An information theory model of hydrophobic interactions

Probing the thermodynamics of competitive ion binding using minimum energy structures

Ion binding is known to affect the properties of biomolecules and is directly involved in many biochemical pathways. Because of the highly polar environments where ions are found, a quantum-mechanical treatment is preferable for understanding the energetics of competitive ion binding. Due to computational cost, a quantum mechanical treatment may involve several approximations, however, whose validity can be difficult to determine. Using thermodynamic cycles, we show how intuitive models for complicated ion binding reactions can be built up from simplified, isolated ion-ligand binding site geometries suitable for quantum mechanical treatment. First, the ion binding free energies of individual, minimum energy structures determine their intrinsic ion selectivities. Next, the relative propensity for each minimum energy structure is determined locally from the balance of ion-ligand and ligand-ligand interaction energies. Finally, the environment external to the binding site exerts its influence both through long-ranged dispersive and electrostatic interactions with the binding site as well as indirectly through shifting the binding site compositional and structural preferences. The resulting picture unifies field-strength, topological control, and phase activation viewpoints into a single theory that explicitly indicates the important role of solute coordination state on overall reaction energetics. As an example, we show that the Na(+) → K(+) selectivities can be recovered by correctly considering the conformational contribution to the selectivity. This can be done even when constraining configuration space to the neighborhood around a single, arbitrarily chosen, minimum energy structure. Structural regions around minima for K(+)- and Na(+)-water clusters are exhibited that display both rigid/mechanical and disordered/entropic selectivity mechanisms for both Na(+) and K(+). Thermodynamic consequences of the theory are discussed with an emphasis on the role of coordination structure in determining experimental properties of ions in complex biological environments.

Computing spatial information from Fourier coefficient distributions

The spatial relationships between molecules can be quantified in terms of information. In the case of membranes, the spatial organization of molecules in a bilayer is closely related to biophysically and biologically important properties. Here, we present an approach to computing spatial information based on Fourier coefficient distributions. The Fourier transform (FT) of an image contains a complete description of the image, and the values of the FT coefficients are uniquely associated with that image. For an image where the distribution of pixels is uncorrelated, the FT coefficients are normally distributed and uncorrelated. Further, the probability distribution for the FT coefficients of such an image can readily be obtained by Parseval's theorem. We take advantage of these properties to compute the spatial information in an image by determining the probability of each coefficient (both real and imaginary parts) in the FT, then using the Shannon formalism to calculate information. By using the probability distribution obtained from Parseval's theorem, an effective distance from the uncorrelated or most uncertain case is obtained. The resulting quantity is an information computed in k-space (kSI). This approach provides a robust, facile and highly flexible framework for quantifying spatial information in images and other types of data (of arbitrary dimensions). The kSI metric is tested on a 2D Ising model, frequently used as a model for lipid bilayer; and the temperature-dependent phase transition is accurately determined from the spatial information in configurations of the system.

Molecular dynamics simulation study of interaction between model rough hydrophobic surfaces

We study some aspects of hydrophobic interaction between molecular rough and flexible model surfaces. The model we use in this work is based on a model we used previously (Eun, C.; Berkowitz, M. L. J. Phys. Chem. B 2009, 113, 13222-13228), when we studied the interaction between model patches of lipid membranes. Our original model consisted of two graphene plates with attached polar headgroups; the plates were immersed in a water bath. The interaction between such plates can be considered as an example of a hydrophilic interaction. In the present work, we modify our previous model by removing the charge from the zwitterionic headgroups. As a result of this procedure, the plate character changes: it becomes hydrophobic. By separating the total interaction (or potential of mean force, PMF) between plates into the direct and the water-mediated interactions, we observe that the latter changes from repulsive to attractive, clearly emphasizing the important role of water as a medium. We also investigate the effect of roughness and flexibility of the headgroups on the interaction between plates and observe that roughness enhances the character of the hydrophobic interaction. The presence of a dewetting transition in a confined space between charge-removed plates confirms that the interaction between plates is strongly hydrophobic. In addition, we notice that there is a shallow local minimum in the PMF in the case of the charge-removed plates. We find that this minimum is associated with the configurational changes that flexible headgroups undergo as the two plates are brought together.

An improved coarse-grained model of solvation and the hydrophobic effect

We present a coarse-grained lattice model of solvation thermodynamics and the hydrophobic effect that implements the ideas of Lum-Chandler-Weeks theory [J. Phys. Chem. B 134, 4570 (1999)] and improves upon previous lattice models based on it. Through comparison with molecular simulation, we show that our model captures the length-scale and curvature dependence of solvation free energies with near-quantitative accuracy and 2-3 orders of magnitude less computational effort, and further, correctly describes the large but rare solvent fluctuations that are involved in dewetting, vapor tube formation, and hydrophobic assembly. Our model is intermediate in detail and complexity between implicit-solvent models and explicit-water simulations.

Ligand binding to protein-binding pockets with wet and dry regions

Biological processes often depend on protein-ligand binding events, yet accurate calculation of the associated energetics remains as a significant challenge of central importance to structure-based drug design. Recently, we have proposed that the displacement of unfavorable waters by the ligand, replacing them with groups complementary to the protein surface, is the principal driving force for protein-ligand binding, and we have introduced the WaterMap method to account this effect. However, in spite of the adage "nature abhors vacuum," one can occasionally observe situations in which a portion of the receptor active site is so unfavorable for water molecules that a void is formed there. In this paper, we demonstrate that the presence of dry regions in the receptor has a nontrivial effect on ligand binding affinity, and suggest that such regions may represent a general motif for molecular recognition between the dry region in the receptor and the hydrophobic groups in the ligands. With the introduction of a term attributable to the occupation of the dry regions by ligand atoms, combined with the WaterMap calculation, we obtain excellent agreement with experiment for the prediction of relative binding affinities for a number of congeneric ligand series binding to the major urinary protein receptor. In addition, WaterMap when combined with the cavity contribution is more predictive than at least one specific implementation [Abel R, Young T, Farid R, Berne BJ, Friesner RA (2008) J Am Chem Soc 130:2817-2831] of the popular MM-GBSA approach to binding affinity calculation.

Probing solvation decay length in order to characterize hydrophobicity-induced bead-bead attractive interactions in polymer chains

In this paper, we quantitatively demonstrate that exponentially decaying attractive potentials can effectively mimic strong hydrophobic interactions between monomer units of a polymer chain dissolved in aqueous solvent. Classical approaches to modeling hydrophobic solvation interactions are based on invariant attractive length scales. However, we demonstrate here that the solvation interaction decay length may need to be posed as a function of the relative separation distances and the sizes of the interacting species (or beads or monomers) to replicate the necessary physical interactions. As an illustrative example, we derive a universal scaling relationship for a given solute-solvent combination between the solvation decay length, the bead radius, and the distance between the interacting beads. With our formalism, the hydrophobic component of the net attractive interaction between monomer units can be synergistically accounted for within the unified framework of a simple exponentially decaying potential law, where the characteristic decay length incorporates the distinctive and critical physical features of the underlying interaction. The present formalism, even in a mesoscopic computational framework, is capable of incorporating the essential physics of the appropriate solute-size dependence and solvent-interaction dependence in the hydrophobic force estimation, without explicitly resolving the underlying molecular level details.

Good practices in free-energy calculations

As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in a wide range of research areas. Yet, the reliability of these calculations can often be improved significantly if a number of precepts, or good practices, are followed. Although the theory upon which these good practices rely has largely been known for many years, it is often overlooked or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. In this contribution, the current best practices for carrying out free-energy calculations using free energy perturbation and nonequilibrium work methods are discussed, demonstrating that at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. Monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway, and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision.

Two mechanisms of ion selectivity in protein binding sites

A theoretical framework is presented to clarify the molecular determinants of ion selectivity in protein binding sites. The relative free energy of a bound ion is expressed in terms of the main coordinating ligands coupled to an effective potential of mean force representing the influence of the rest of the protein. The latter is separated into two main contributions. The first includes all the forces keeping the ion and the coordinating ligands confined to a microscopic subvolume but does not prevent the ligands from adapting to a smaller or larger ion. The second regroups all the remaining forces that control the precise geometry of the coordinating ligands best adapted to a given ion. The theoretical framework makes it possible to delineate two important limiting cases. In the limit where the geometric forces are dominant (rigid binding site), ion selectivity is controlled by the ion-ligand interactions within the matching cavity size according to the familiar "snug-fit" mechanism of host-guest chemistry. In the limit where the geometric forces are negligible, the ion and ligands behave as a "confined microdroplet" that is free to fluctuate and adapt to ions of different sizes. In this case, ion selectivity is set by the interplay between ion-ligand and ligand-ligand interactions and is controlled by the number and the chemical type of ion-coordinating ligands. The framework is illustrated by considering the ion-selective binding sites in the KcsA channel and the LeuT transporter.

On the molecular origin of cold denaturation of globular proteins

A polypeptide chain can adopt very different conformations, a fundamental distinguishing feature of which is the water accessible surface area, WASA, that is a measure of the layer around the polypeptide chain where the center of water molecules cannot physically enter, generating a solvent-excluded volume effect. The large WASA decrease associated with the folding of a globular protein leads to a large decrease in the solvent-excluded volume, and so to a large increase in the configurational/translational freedom of water molecules. The latter is a quantity that depends upon temperature. Simple calculations over the -30 to 150 °C temperature range, where liquid water can exist at 1 atm, show that such a gain decreases significantly on lowering the temperature below 0 °C, paralleling the decrease in liquid water density. There will be a temperature where the destabilizing contribution of the polypeptide chain conformational entropy exactly matches the stabilizing contribution of the water configurational/translational entropy, leading to cold denaturation.

Hydration in discrete water. A mean field, cellular automata based approach to calculating hydration free energies

A simple, semiheuristic solvation model based on a discrete, BCC grid of solvent cells has been presented. The model utilizes a mean field approach for the calculation of solute-solvent and solvent-solvent interaction energies and a cellular automata based algorithm for the prediction of solvent distribution in the presence of solute. The construction of the effective Hamiltonian for a solvent cell provides an explicit coupling between orientation-dependent water-solute electrostatic interactions and water-water hydrogen bonding. The water-solute dispersion interaction is also explicitly taken into account. The model does not depend on any arbitrary definition of the solute-solvent interface nor does it use a microscopic surface tension for the calculation of nonpolar contributions to the hydration free energies. It is demonstrated that the model provides satisfactory predictions of hydration free energies for drug-like molecules and is able to reproduce the distribution of buried water molecules within protein structures. The model is computationally efficient and is applicable to arbitrary molecules described by atomistic force field.

A statistical mechanical theory for a two-dimensional model of water

We develop a statistical mechanical model for the thermal and volumetric properties of waterlike fluids. Each water molecule is a two-dimensional disk with three hydrogen-bonding arms. Each water interacts with 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 the Truskett and Dill (TD) treatment of the "Mercedes-Benz" (MB) model. The present model gives better predictions than TD for hydrogen-bond populations in liquid water by distinguishing strong cooperative hydrogen bonds from weaker ones. We explore properties versus temperature T and pressure p. We find that the volumetric and thermal properties follow the same trends with T as real water and are in good general agreement with Monte Carlo simulations of MB water, including the density anomaly, the minimum in the isothermal compressibility, and the decreased number of hydrogen bonds for increasing temperature. The model reproduces that pressure squeezes out water's heat capacity and leads to a negative thermal expansion coefficient at low temperatures. In terms of water structuring, the variance in hydrogen-bonding angles increases with both T and p, while the variance in water density increases with T but decreases with p. Hydrogen bonding is an energy storage mechanism that leads to water's large heat capacity (for its size) and to the fragility in its cagelike structures, which are easily melted by temperature and pressure to a more van der Waals-like liquid state.

How Can Hydrophobic Association Be Enthalpy Driven?

Hydrophobic association is often recognized as being driven by favorable entropic contributions. Here, using explicit solvent molecular dynamics simulations we investigate binding in a model hydrophobic receptor-ligand system which appears, instead, to be driven by enthalpy and opposed by entropy. We use the temperature dependence of the potential of mean force to analyze the thermodynamic contributions along the association coordinate. Relating such contributions to the ongoing changes in system hydration allows us to demonstrate that the overall binding thermodynamics is determined by the expulsion of disorganized water from the receptor cavity. Our model study sheds light on the solvent-induced driving forces for receptor-ligand association of general, transferable relevance for biological systems with poorly hydrated binding sites.

Solvation theory to provide a molecular interpretation of the hydrophobic entropy loss of noble-gas hydration

An equation for the chemical potential of a dilute aqueous solution of noble gases is derived in terms of energies, force and torque magnitudes, and solute and water coordination numbers, quantities which are all measured from an equilibrium molecular dynamics simulation. Also derived are equations for the Gibbs free energy, enthalpy and entropy of hydration for the Henry's law process, the Ostwald process, and a third proposed process going from an arbitrary concentration in the gas phase to the equivalent mole fraction in aqueous solution which has simpler expressions for the enthalpy and entropy changes. Good agreement with experimental hydration free energies is obtained in the TIP4P and SPC/E water models although the solute's force field appears to affect the enthalpies and entropies obtained. In contrast to other methods, the approach gives a complete breakdown of the entropy for every degree of freedom and makes possible a direct structural interpretation of the well-known entropy loss accompanying the hydrophobic hydration of small non-polar molecules under ambient conditions. The noble-gas solutes experience only a small reduction in their vibrational entropy, with larger solutes experiencing a greater loss. The vibrational and librational entropy components of water actually increase but only marginally, negating any idea of water confinement. The term that contributes the most to the hydrophobic entropy loss is found to be water's orientational term which quantifies the number of orientational minima per water molecule and how many ways the whole hydrogen-bond network can form. These findings help resolve contradictory deductions from experiments that water structure around non-polar solutes is similar to bulk water in some ways but different in others. That the entropy loss lies in water's rotational entropy contrasts with other claims that it largely lies in water's translational entropy, but this apparent discrepancy arises because of different coordinate definitions and reference frames used to define the entropy terms.

Hydrophobic collapse and cold denaturation in the Jagla model of water

The Jagla model is a coarse-grained model of water which describes interactions between groups of water molecules by a spherically symmetric potential characterized by a hard core, a linear repulsive ramp and a long-range attractive ramp. The Jagla model qualitatively reproduces the thermodynamics and dynamics of liquid water including density and diffusion anomalies as well as certain chemical properties such the increase of solubility of small hydrophobic particles upon cooling. We examine, via molecular dynamics simulation, the behavior of the bead-on-a-string polymers of various lengths in the Jagla model. We find that such polymers exhibit swelling upon cooling similar to cold denaturation of proteins in water. We show that while for short polymers the swelling is gradual, longer polymers exhibit a first-order-like phase transition between a globular phase at high temperatures to a random coil state at cold temperatures. This transition is associated with the formation of a liquid-polymer phase boundary surrounding the globule and complete dewetting of the central parts of the globule at high temperatures. We study thermodynamics of this transition and find that the entropy, volume, and potential energy of the solvent-random coil system is lower than those of the globule-solvent system. Accordingly the slope of the coil-globule transition line on a PT plane has positive slope. We present simple thermodynamic considerations similar to classical nucleation theory, which relate the temperature of the cold swelling transition to polymer length and relate the dewetting of the globule to its diameter and to the Egelstaff-Widom length scale.

Role of electrostatics in modulating hydrophobic interactions and barriers to hydrophobic assembly

Hydrophobic effects continue to be an active area of research due to implications for a wide range of physicochemical phenomena. Molecular dynamics simulations have been used extensively in the study of such effects using various water potential models, with few studies addressing the differences between models. In particular, studies considering the explicit treatment of water polarizability are underrepresented in the literature. We present results from molecular dynamics simulations that systematically compare the dependence of large-scale hydrophobic effects on the water model. We consider three common nonpolarizable models (SPC/E, TIP3P, and TIP4P) and two common polarizable models (TIP4P-FQ and SWM4-NDP). Results highlight the similarities and differences of the different water models in the vicinity of two large hydrophobic plates. In particular, profiles of average density, density fluctuations, orientation, and hydrogen bonding show only minor differences among the water models studied. However, the potential of mean force for the hydrophobe dimerization is significantly reduced in the polarizable water systems. TIP4P-FQ shows the deepest minimum of approximately -54(+/-3) kcal/mol compared to -40(+/-3), -40(+/-2), -42(+/-3), and -45(+/-5) kcal/mol for TIP4P, TIP3P, SPC/E, and SWM4-NDP (all relative to the dissociated state). We discuss the relationship between hydrophobic association and the strength of water-water interactions in the liquid phase. Results suggest that models treating polarizability (both implicitly and explicitly) influence a stronger driving force toward hydrophobic assembly. Implications of these results, as well as prospectives on future work, are discussed.

Effect of hydrophobic solutes on the liquid-liquid critical point

Jagla ramp particles, interacting through a ramp potential with two characteristic length scales, are known to show in their bulk phase thermodynamic and dynamic anomalies, similar to what is found in water. Jagla particles also exhibit a line of phase transitions separating a low density liquid phase and a high density liquid phase, terminating in a liquid-liquid critical point in a region of the phase diagram that can be studied by simulations. Employing molecular dynamics computer simulations, we study the thermodynamics and the dynamics of solutions of hard spheres (HS) in a solvent formed by Jagla ramp particles. We consider the cases of HS mole fraction xHS=0.10, 0.15, and 0.20, and also the case xHS=0.50 (a 1:1 mixture of HS and Jagla particles). We find a liquid-liquid critical point, up to the highest HS mole fraction; its position shifts to higher pressures and lower temperatures upon increasing xHS. We also find that the diffusion coefficient anomalies appear to be preserved for all the mole fractions studied.

Unfolding of hydrophobic polymers in guanidinium chloride solutions

Guanidinium chloride (GdmCl) is a widely used chemical denaturant that unfolds proteins. Its effects on hydrophobic interactions are, however, not fully understood. We quantify the effects of GdmCl on various manifestations of hydrophobicity--from solvation and interactions of small solutes to folding-unfolding of hydrophobic polymers--in water and in concentrated GdmCl solutions. For comparison, we also perform similar calculations in solutions of NaCl and CsCl in water. Like NaCl and CsCl, GdmCl increases the surface tension of water, decreases the solubility of small hydrophobic solutes, and enhances the strength of hydrophobic interactions at the pair level. However, unlike NaCl and CsCl, GdmCl destabilizes folded states of hydrophobic polymers. We show that Gdm(+) ions preferentially coat the hydrophobic polymer, and it is the direct van der Waals interaction between Gdm(+) ions and the polymer that contributes to the destabilization of folded states. Interestingly, the temperature dependence of the free energy of unfolding of the hydrophobic polymer in water is protein-like, with signatures of both heat and cold denaturation. Addition of GdmCl shifts the cold denaturation temperature higher, into the experimentally accessible region. Finally, translational as well as conformational dynamics of the polymer are slower in GdmCl and correlate with dynamics of water molecules in solution.

Charge, hydrophobicity, and confined water: putting past simulations into a simple theoretical framework

Water permeates all life, and mediates forces that are essential to the process of macromolecular self-assembly. Predicting these forces in a given biological context is challenging, since water organizes itself differently next to charged and hydrophobic surfaces, both of which are typically at play on the nanoscale in vivo. In this work, we present a simple statistical mechanical model for the forces water mediates between different confining surfaces, and demonstrate that the model qualitatively unifies a wide range of phenomena known in the simulation literature, including several cases of protein folding under confinement.

Ultrafast imaging and the phase problem for inelastic X-ray scattering

A new method for imaging ultrafast dynamics in condensed matter using inelastic X-ray scattering (IXS) is described. Using the concepts of causality and irreversibility a general solution to the inverse scattering problem (or "phase problem") for IXS is illustrated, which enables direct imaging of dynamics of the electron density with resolutions of approximately 1 attosecond (10(-18) s) in time and <1 A in space. This method is not just Fourier transformation of the IXS data, but a means to impose causality on the data and reconstruct the charge propagator. The method can also be applied to inelastic electron or neutron scattering. A general outline of phenomena that can and cannot be studied with this technique and an outlook for the future is provided.

Explicit and implicit modeling of nanobubbles in hydrophobic confinement

Water at normal conditions is a fluid thermodynamically close to the liquid-vapor phase coexistence and features a large surface tension. This combination can lead to interesting capillary phenomena on microscopic scales. Explicit water molecular dynamics (MD) computer simulations of hydrophobic solutes, for instance, give evidence of capillary evaporation on nanometer scales, i.e., the formation of nanometer-sized vapor bubbles (nanobubbles) between confining hydrophobic surfaces. This phenomenon has been exemplified for solutes with varying complexity, e.g., paraffin plates, coarse-grained homopolymers, biological and solid-state channels, and atomistically resolved proteins. It has been argued that nanobubbles strongly impact interactions in nanofluidic devices, translocation processes, and even in protein stability, function, and folding. As large-scale MD simulations are computationally expensive, the efficient multiscale modeling of nanobubbles and the prediction of their stability poses a formidable task to the'nanophysical' community. Recently, we have presented a conceptually novel and versatile implicit solvent model, namely, the variational implicit solvent model (VISM), which is based on a geometric energy functional. As reviewed here, first solvation studies of simple hydrophobic solutes using VISM coupled with the numerical level-set scheme show promising results, and, in particular, capture nanobubble formation and its subtle competition to local energetic potentials in hydrophobic confinement.

Theoretical investigations of nitric oxide channeling in Mycobacterium tuberculosis truncated hemoglobin N

Mycobacterium tuberculosis group I truncated hemoglobin trHbN catalyzes the oxidation of nitric oxide (NO) to nitrate with a second-order rate constant k approximately 745 microM(-1) s(-1) at 23 degrees C (nitric oxide dioxygenase reaction). It was proposed that this high efficiency is associated with the presence of hydrophobic tunnels inside trHbN structure that allow substrate diffusion to the distal heme pocket. In this work, we investigated the mechanisms of NO diffusion within trHbN tunnels in the context of the nitric oxide dioxygenase reaction using two independent approaches. Molecular dynamics simulations of trHbN were performed in the presence of explicit NO molecules. Successful NO diffusion from the bulk solvent to the distal heme pocket was observed in all simulations performed. The simulations revealed that NO interacts with trHbN at specific surface sites, composed of hydrophobic residues located at tunnel entrances. The entry and the internal diffusion of NO inside trHbN were performed using the Long, Short, and EH tunnels reported earlier. The Short tunnel was preferentially used by NO to reach the distal heme pocket. This preference is ascribed to its hydrophobic funnel-shape entrance, covering a large area extending far from the tunnel entrance. This funnel-shape entrance triggers the frequent formation of solvent-excluded cavities capable of hosting up to three NO molecules, thereby accelerating NO capture and entry. The importance of hydrophobicity of entrances for NO capture is highlighted by a comparison with a polar mutant for which residues at entrances were mutated with polar residues. A complete map of NO diffusion pathways inside trHbN matrix was calculated, and NO molecules were found to diffuse from Xe cavity to Xe cavity. This scheme was in perfect agreement with the three-dimensional free-energy distribution calculated using implicit ligand sampling. The trajectories showed that NO significantly alters the dynamics of the key amino acids of Phe(62)(E15), a residue proposed to act as a gate controlling ligand traffic inside the Long tunnel, and also of Ile(119)(H11), at the entrance of the Short tunnel. It is noteworthy that NO diffusion inside trHbN tunnels is much faster than that reported previously for myoglobin. The results presented in this work shed light on the diffusion mechanism of apolar gaseous substrates inside protein matrix.

Fluctuations of water near extended hydrophobic and hydrophilic surfaces

We use molecular dynamics simulations of the SPC-E model of liquid water to derive probability distributions for water density fluctuations in probe volumes of different shapes and sizes, both in the bulk as well as near hydrophobic and hydrophilic surfaces. Our results are obtained with a biased sampling of coarse-grained densities that is easily combined with molecular dynamics integration algorithms. Our principal result is that the probability for density fluctuations of water near a hydrophobic surface, with or without surface water attractions, is akin to density fluctuations at the water-vapor interface. Specifically, the probability of density depletion near the surface is significantly larger than that in the bulk, and this enhanced probability is responsible for hydrophobic forces of assembly. In contrast, we find that the statistics of water density fluctuations near a model hydrophilic surface are similar to that in the bulk.

Oil/water transfer is partly driven by molecular shape, not just size

We present a new approach to computer modeling of solvation free energies of oil in water. In Semi-Explicit Assembly, we first precompute structural and thermal properties of TIP3P waters around different Lennard-Jones spheres. This tabulated information is then used to compute the nonpolar solvation properties of arbitrary solutes. By accumulating interactions from whole regions of the solute molecule, Semi-Explicit Assembly more properly accounts for effects of solute shape and solves problems that appear as nonadditivities in traditional gammaA approaches. Semi-Explicit Assembly involves little parameter fitting because the solute and water properties are taken from existing force fields. We tested the predictions on alkanes, alkynes, linear and planar polyaromatic hydrocarbons, and on a diverse set of 504 molecules previously explored by explicit solvent simulations. We found that not all hydrocarbons are the same. Hydrocarbons have "hot spots", places where first-shell waters interact more strongly with the molecule than at other locations. For example, waters are more attracted to hover over hydrocarbon rings than at the edges. By accounting for these collective regional effects, Semi-Explicit Assembly approaches the physical accuracies of explicit solvent models in computing nonpolar solvation free energies, but because of the precomputations and the regional additivities, it is nearly as fast to compute as gammaA methods.

Hydration dynamics at femtosecond time scales and angstrom length scales from inelastic x-ray scattering

We use high resolution dynamical structure factor S(q,omega) data measured with inelastic x-ray scattering to reconstruct the Green's function of water, which describes its density response to a point charge, and provides a fundamental comparative model for solvation behavior at molecular time scales and length scales. Good agreement is found with simulations, scattering and spectroscopic experiments. These results suggest that a moving point charge will modify its hydration structure, evolving from a spherical closed shell to a steady-state cylindrical hydration "sleeve".

Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions

The venerable theory of electrokinetic phenomena rests on the hypothesis of a dilute solution of point-like ions in quasi-equilibrium with a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage (kT/e approximately 25 mV at room temperature). In nonlinear electrokinetic phenomena, such as AC or induced-charge electro-osmosis (ACEO, ICEO) and induced-charge electrophoresis (ICEP), several V approximately 100 kT/e are applied to polarizable surfaces in microscopic geometries, and the resulting electric fields and induced surface charges are large enough to violate the assumptions of the classical theory. In this article, we review the experimental and theoretical literatures, highlight discrepancies between theory and experiment, introduce possible modifications of the theory, and analyze their consequences. We argue that, in response to a large applied voltage, the "compact layer" and "shear plane" effectively advance into the liquid, due to the crowding of counterions. Using simple continuum models, we predict two general trends at large voltages: (i) ionic crowding against a blocking surface expands the diffuse double layer and thus decreases its differential capacitance, and (ii) a charge-induced viscosity increase near the surface reduces the electro-osmotic mobility; each trend is enhanced by dielectric saturation. The first effect is able to predict high-frequency flow reversal in ACEO pumps, while the second may explain the decay of ICEO flow with increasing salt concentration. Through several colloidal examples, such as ICEP of an uncharged metal sphere in an asymmetric electrolyte, we show that nonlinear electrokinetic phenomena are generally ion-specific. Similar theoretical issues arise in nanofluidics (due to confinement) and ionic liquids (due to the lack of solvent), so the paper concludes with a general framework of modified electrokinetic equations for finite-sized ions.

Hydration structures near finite-sized nanoscopic objects reconstructed using inelastic x-ray scattering measurements

Recent work has shown that it is possible to use high resolution dynamical structure factor S(q,ω) data measured with inelastic x-ray scattering to reconstruct the Green's function of water, which describes its dynamical density response to a point charge. Here, we generalize this approach and describe a strategy for reconstructing hydration behavior near simple charge distributions with excluded volumes, with the long term goal of engaging hydration processes in complex molecular systems. We use this Green's function based imaging of dynamics method to generate hydration structures and show that they are consistent with those of well-studied model systems.

How Does Solute-Polarization Affect the Hydrophobic Hydration of Methane?

We simulate the solubility and solvation free energy of methane dissolved in water at infinite dilution. Molecular dynamics simulations of TIP4P-Ew model water are carried out at ambient pressure conditions over a large temperature interval, ranging from 250 K to 370 K. Solvation free energies are determined using the Widom particle insertion method. The fitted temperature dependent data is used to calculate solvation enthalpies, entropies, as well as the heat capacity of solvation. In particular we study the effect of polarizability of methane on those thermodynamic parameters. Solute polarization leads to a lowering of the solvation free energy at 298 K to 8.3 kJ mol−1, almost exactly matching the experimental value. A close inspection of the enthalpic and entropic contributions, however, reveals that this coincidence is a consequence of a compensation of enthalpic and entropic contributions, each of them deviating even larger from their respective experimental values. Surprisingly, the solute polarizability is apparently affecting the solvation entropy more strongly than the solvation enthalpy, leading to an about 5 J K−1 mol−1 smaller (less negative) solvation entropy compared to the non-polarizable model. The solute-water radial distribution functions of the polarizable particle reveals significant modifications, favoring small distances, as well as structural changes, very similar to those caused by a temperature increase. This is suggesting that the reduced negative solvation entropy of a polarizable methane particle is related to a more disordered, "high-temperature"-like hydration shell.

Hydrophobic interactions of hexane in nanosized water droplets

We use all-atomistic molecular dynamics simulations to study hydrophobic interactions of hexane in nanosized water droplets where the hydrogen bonding network of water molecules is disrupted at the surface. As a result of the competition between the energetics of a hexane molecule and the distribution of water molecules that lost the ability to form hydrogen bonds at the boundary, all-trans-hexane molecules are statistically favored at the surface of a nanosized water droplet and such a statistical trend increases as the size of a nano water droplet decreases. Changes in the radial distribution and the orientation of water molecules surrounding hexane in nanosized water droplets over bulk water are indicative of the finite-size effects on the structural distribution of a short, topologically complex hydrocarbon chain.

Characterizing hydrophobicity of interfaces by using cavity formation, solute binding, and water correlations

Hydrophobicity is often characterized macroscopically by the droplet contact angle. Molecular signatures of hydrophobicity have, however, remained elusive. Successful theories predict a drying transition leading to a vapor-like region near large hard-sphere solutes and interfaces. Adding attractions wets the interface with local density increasing with attractions. Here we present extensive molecular simulation studies of hydration of realistic surfaces with a wide range of chemistries from hydrophobic (-CF(3), -CH(3)) to hydrophilic (-OH, -CONH(2)). We show that the water density near weakly attractive hydrophobic surfaces (e.g., -CF(3)) can be bulk-like or larger, and provides a poor quantification of surface hydrophobicity. In contrast, the probability of cavity formation or the free energy of binding of hydrophobic solutes to interfaces correlates quantitatively with the macroscopic wetting properties and serves as an excellent signature of hydrophobicity. Specifically, the probability of cavity formation is enhanced in the vicinity of hydrophobic surfaces, and water-water correlations correspondingly display characteristics similar to those near a vapor-liquid interface. Hydrophilic surfaces suppress cavity formation and reduce the water-water correlation length. Our results suggest a potentially robust approach for characterizing hydrophobicity of more complex and heterogeneous surfaces of proteins and biomolecules, and other nanoscopic objects.

Why water reorientation slows without iceberg formation around hydrophobic solutes

The dynamics of water molecules next to hydrophobic solutes is investigated, specifically addressing the recent controversy raised by the first time-resolved observations, which concluded that some water molecules are immobilized by hydrophobic groups, in strong contrast to previous NMR conclusions. Through molecular dynamics simulations and an analytic jump reorientation model, we identify the water reorientation mechanism next to a hydrophobic solute and provide evidence that no water molecules are immobilized by hydrophobic solutes. Their moderate rotational slowdown compared to bulk water (e.g., by a factor of less than 2 at low solute concentration) is mainly due to slower hydrogen-bond exchange. The slowdown is quantitatively described by a solute excluded volume effect at the transition state for the key hydrogen-bond exchange in the reorientation mechanism. We show that this picture is consistent with both ultrafast anisotropy and NMR experimental results and that the transition state excluded volume theory yields quantitative predictions of the rotational slowdown for diverse hydrophobic solutes of varying size over a wide concentration range. We also explain why hydrophobic groups slow water reorientation less than do some hydrophilic groups.

The relative entropy is fundamental to multiscale and inverse thermodynamic problems

We show that the relative entropy, S(rel) identical with Sigma(p(T)) ln(p(T)/p(M)), provides a fundamental and unifying framework for multiscale analysis and for inverse molecular-thermodynamic problems involving optimization of a model system (M) to reproduce the properties of a target one (T). We demonstrate that the relative entropy serves as a generating function for principles in variational mean-field theory and uniqueness and gives intuitive results for simple case scenarios in model development. Moreover, we suggest that the relative entropy provides a rigorous framework for multiscale simulations and offers new numerical techniques for linking models at different scales. Finally, we show that S(rel) carries physical significance by using it to quantify the deviations of a three-site model of water from simple liquids, finding that the relative entropy, a thermodynamic concept, even predicts water's kinetic anomalies.