The Hydrophobic Effect and the Influence of Solute−Solvent Attractions

An Update on Theoretical and Metrological Aspects of the Surface Hydrophobicity of Virus and Virus-Like Particles

Viruses are biological entities embodied in protein-based nanoparticles devoid of metabolic activity. Hence, the colloidal, interfacial, and chemical reactivity of virus particles (VPs) profoundly affects the fate of natural and artificial viruses in biotic or abiotic aqueous systems. These rely on the physical chemistry at the outer surface of VPs. In other words, whether wild or synthetic VPs and regardless of the scientific fields involved, taming viruses implies thus managing the physical chemistry at the VP external surface. The surface hydrophobicity (SH) of VPs is a critical feature that must be looked at. Still, the literature dealing with nanoscale hydrophobic domains at the proteinaceous surface of VPs underlying their global SH is like a fragmented puzzle. This article provides an overview of the topic from the perspective of modern protein biophysics for updating the classic physicochemical picture of outer VP/water interfaces hitherto accepted. Patterns of non-polar and "false-polar" patches, expressing variable hydrophobic degrees according to neighboring polar patches, are now drawn. The extensive discussion of reviewed data generates such fresh ideas to explore in the coming years for better modeling the SH of wild virions or engineered virus-based nanoparticles, paving the way for new directions in fundamental virology and virus-based chemistry.

A classical density functional theory for solvation across length scales

A central aim of multiscale modeling is to use results from the Schrödinger equation to predict phenomenology on length scales that far exceed those of typical molecular correlations. In this work, we present a new approach rooted in classical density functional theory (cDFT) that allows us to accurately describe the solvation of apolar solutes across length scales. Our approach builds on the Lum-Chandler-Weeks (LCW) theory of hydrophobicity [K. Lum et al., J. Phys. Chem. B 103, 4570 (1999)] by constructing a free energy functional that uses a slowly varying component of the density field as a reference. From a practical viewpoint, the theory we present is numerically simpler and generalizes to solutes with soft-core repulsion more easily than LCW theory. Furthermore, by assessing the local compressibility and its critical scaling behavior, we demonstrate that our LCW-style cDFT approach contains the physics of critical drying, which has been emphasized as an essential aspect of hydrophobicity by recent theories. As our approach is parameterized on the two-body direct correlation function of the uniform fluid and the liquid-vapor surface tension, it straightforwardly captures the temperature dependence of solvation. Moreover, we use our theory to describe solvation at a first-principles level on length scales that vastly exceed what is accessible to molecular simulations.

How do water-mediated interactions and osmotic second virial coefficients vary with particle size?

We examine quantitatively the solute-size dependences of the effective interactions between nonpolar solutes in water and in a simple liquid. The potential w(r) of mean force and the osmotic second virial coefficients B are calculated with high accuracy from molecular dynamics simulations. As the solute diameter increases from methane's to C60's with the solute-solute and solute-solvent attractive interaction parameters fixed to those for the methane-methane and methane-water interactions, the first minimum of w(r) lowers from -1.1 to -4.7 in units of the thermal energy kT. Correspondingly, the magnitude of B (<0) increases proportional to σα with some power close to 6 or 7, which reinforces the solute-size dependence of B found earlier for a smaller range of σ [H. Naito, R. Okamoto, T. Sumi and K. Koga, J. Chem. Phys., 2022, 156, 221104]. We also demonstrate that the strength of the attractive interactions between solute and solvent molecules can qualitatively change the characteristics of the effective pair interaction between solute particles, both in water and in a simple liquid. If the solute-solvent attractive force is set to be weaker (stronger) than a threshold, the effective interaction becomes increasingly attractive (repulsive) with increasing solute size.

Thermodynamics perturbation theory for solvation of nonpolar solutes in rose model

A simple model of water, called the rose model, is used in this work. The rose model is a very simple model that can provide insight into the anomalous properties of water. In the rose water model, the molecules are represented as two-dimensional Lennard-Jones disks with potentials for orientation-dependent pairwise interactions mimicking formations of hydrogen bonds. We have recently applied a Wertheim integral equation theory (IET) and a thermodynamic perturbation theory (TPT) to the rose model in bulk. These analytical theories offer the advantage of being computationally less intensive than computer simulations by orders of magnitudes. Here we have applied the TPT to study the transfer of a nonpolar solute into rose water, the so-called hydrophobic effect. Similarly as in our previous work for bulk water, we have found that the theory reproduces the computer simulation results quite well at higher temperatures, while the theories predict the qualitative trends at low temperatures.

Simple Model of Liquid Water Dynamics

We develop an analytical statistical-mechanical model to study the dynamic properties of liquid water. In this two-dimensional model, neighboring waters can interact through a hydrogen bond, a van der Waals contact, or an ice-like cage structure or have no interaction. We calculate the diffusion coefficient, viscosity, and thermal conductivity versus temperature and pressure. The trends follow those seen in the water experiments. The model explains that in warm water, heating drives faster diffusion but less interaction, so the viscosity and conductivity decrease. Cooling cold water causes poorer energy exchange because water's ice-like cages are big and immobile and collide infrequently. The main antagonism in water dynamics is not between vdW and H bonds, but it is an interplay between both those pair interactions, multibody cages, and no interaction. The value of this simple model is that it is analytical, so calculations are immediate, and it gives interpretations based on molecular physics.

Local solvation structures govern the mixing thermodynamics of glycerol-water solutions

Glycerol is a major cryoprotective agent and is widely used to promote protein stabilization. By a combined experimental and theoretical study, we show that global thermodynamic mixing properties of glycerol and water are dictated by local solvation motifs. We identify three hydration water populations, i.e., bulk water, bound water (water hydrogen bonded to the hydrophilic groups of glycerol) and cavity wrap water (water hydrating the hydrophobic moieties). Here, we show that for glycerol experimental observables in the THz regime allow quantification of the abundance of bound water and its partial contribution to the mixing thermodynamics. Specifically, we uncover a 1 : 1 connection between the population of bound waters and the mixing enthalpy, which is further corroborated by the simulation results. Therefore, the changes in global thermodynamic quantity - mixing enthalpy - are rationalized at the molecular level in terms of changes in the local hydrophilic hydration population as a function of glycerol mole fraction in the full miscibility range. This offers opportunities to rationally design polyol water, as well as other aqueous mixtures to optimize technological applications by tuning mixing enthalpy and entropy based on spectroscopic screening.

Unraveling the hydrophobic interaction mechanisms of hydrocarbon and fluorinated surfaces

HYPOTHESIS

Numerous hydrocarbon and fluorine-based hydrophobic surfaces have been widely applied in various engineering and bioengineering fields. It is hypothesized that the hydrophobic interactions of hydrocarbon and fluorinated surfaces in aqueous media would show some differences.

EXPERIMENTS

The hydrophobic interactions of hydrocarbon and fluorinated surfaces with air bubbles in aqueous solutions have been systematically and quantitatively measured using a bubble probe atomic force microscopy (AFM) technique. Ethanol was introduced to water for modulating the solution polarity. The experimental force profiles were analyzed using a theoretical model combining the Reynolds lubrication theory and augmented Young-Laplace equation by including disjoining pressure arisen from the Derjarguin-Landau-Verwey-Overbeek (DLVO) and non-DLVO interactions (i.e., hydrophobic interactions).

FINDINGS

The experiment results show that the hydrophobic interactions were firstly weakened and then strengthened by increasing ethanol content in the aqueous media, mainly due to the variation in interfacial hydrogen bonding network. The fluorinated surface exhibited less sensitivity to ethanol than hydrocarbon surface, which is attributed to the presence of ordered interfacial water layer. Our work reveals the different hydrophobic effects of hydrocarbon and fluorinated surfaces, with useful implications on modulating the interfacial interactions of relevant materials in various engineering and bioengineering applications.

Single-Molecule Force Spectroscopy Reveals Cation-π Interactions in Aqueous Media Are Highly Affected by Cation Dehydration

Cation-π interactions underlie many important processes in biology and materials science. However, experimental investigations of cation-π interactions in aqueous media remain challenging. Here, we studied the cation-π binding strength and mechanism by pulling two hydrophobic polymers with distinct cation binding properties, i.e., poly-pentafluorostyrene and polystyrene, in aqueous media using single-molecule force spectroscopy and nuclear magnetic resonance measurement. We found that the interaction strengths linearly depend on the cation concentrations, following the order of Li^{+}<NH_{4}^{+}<Na^{+}<K^{+}. The binding energies are 0.03-0.23  kJ mol^{-1} M^{-1}. This order is distinct from the strength of cation-π interactions in gas phase and may be caused by the different dehydration ability of the cations. Taken together, our method provides a unique perspective to investigate cation-π interactions under physiologically relevant conditions.

The electric field changes the anomalous properties of the Mercedes Benz water model

The influence of a homogeneous constant electric field on water properties was assessed. We used a simple two-dimensional statistical mechanical model called the Mercedes-Benz (MB) model of water in the study. The MB water molecules are two-dimensional disks with Gaussian arms that mimic the formation of hydrogen bonds. The model is modified with added charges for interaction with the electric field. The influence of the strength of the electric field on the water's properties was studied using Monte Carlo simulations. The structure and thermodynamics of the water were determined as a function of the strength of the electric field. We observed that the properties and phase transitions of the water in the low strength electric field does not change. In contrast, the high strength electric field shifts boiling and melting points as well as the position of the density maxima. After further increasing the strength of the electric field the density anomaly disappears.

Understanding the physics of hydrophobic solvation

Simulations of water near extended hydrophobic spherical solutes have revealed the presence of a region of depleted density and accompanying enhanced density fluctuations. The physical origin of both phenomena has remained somewhat obscure. We investigate these effects employing a mesoscopic binding potential analysis, classical density functional theory (DFT) calculations for a simple Lennard-Jones solvent, and Grand Canonical Monte Carlo (GCMC) simulations of a monatomic water (mw) model. We argue that the density depletion and enhanced fluctuations are near-critical phenomena. Specifically, we show that they can be viewed as remnants of the critical drying surface phase transition that occurs at bulk liquid-vapor coexistence in the macroscopic planar limit, i.e., as the solute radius R_s → ∞. Focusing on the radial density profile ρ(r) and a sensitive spatial measure of fluctuations, the local compressibility profile χ(r), our binding potential analysis provides explicit predictions for the manner in which the key features of ρ(r) and χ(r) scale with R_s, the strength of solute-water attraction ɛ_sf, and the deviation from liquid-vapor coexistence of the chemical potential, δμ. These scaling predictions are confirmed by our DFT calculations and GCMC simulations. As such, our theory provides a firm basis for understanding the physics of hydrophobic solvation.

Isotope effects observed in diluted D2O/H2O mixtures identify HOD-induced low-density structures in D2O but not H2O

Normal and heavy water are solvents most commonly used to study the isotope effect. The isotope effect of a solvent significantly influences the behavior of a single molecule in a solution, especially when there are interactions between the solvent and the solute. The influence of the isotope effect becomes more significant in D₂O/H₂O since the hydrogen bond in H₂O is slightly weaker than its counterpart (deuterium bond) in D₂O. Herein, we characterize the isotope effect in a mixture of normal and heavy water on the solvation of a HOD molecule. We show that the HOD molecule affects the proximal solvent molecules, and these disturbances are much more significant in heavy water than in normal water. Moreover, in D₂O, we observe the formation of low-density structures indicative of an ordering of the solvent around the HOD molecule. The qualitative differences between HOD interaction with D₂O and H₂O were consistently confirmed with Raman spectroscopy and NMR diffusometry.

Correlation lengths in nanoconfined water and transport properties

We report the existence of disparate static and dynamic correlation lengths that could describe the influence of confinement on nanoconfined water (NCW). Various aspects of viscous properties, such as anisotropy and viscoelasticity, of NCW are studied by varying the separation distance "d" between two confining hydrophobic plates. The transverse component of the mean square stress exhibits slow spatial decay (measured from the surface) beyond ∼1.8 nm, which was not reported before. The static correlation length obtained from fitting the exponential decay of the transverse mean-square stress with d is 0.75 nm, while the decay time of the stress-stress time correlation function gives a dynamic correlation length of only 0.35 nm. The shortness of the dynamic correlation length seems to arise from the low sensitivity of orientational relaxation to confinement. In the frequency-dependent viscosity, we observe a new peak at about 50 cm^-1 that is not present in the bulk. This new peak is prominent even at 3 nm separations. The peak is absent in the bulk, although it is close to the intermolecular -O-O-O- bending mode well known in liquid water. We further explore the relationship between diffusion and viscosity in NCW by varying d.

Osmotic second virial coefficients for hydrophobic interactions as a function of solute size

To gain quantitative insight into how the overall strength of the hydrophobic interaction varies with the molecular size, we calculate osmotic second virial coefficients B for hydrophobic spherical molecules of different diameters σ in water based on molecular simulation with corrections to the finite-size and finite-concentration effects. It is shown that B (<0) changes by two orders of magnitude greater as σ increases twofold and its solute-size dependence is best fit by a power law B ∝ σ^α with the exponent α ≃ 6, which contrasts with the cubic power law that the second virial coefficients of gases obey. It is also found that values of B for the solutes in a nonpolar solvent are positive but they obey the same power law as in water. A thermodynamic identity for B derived earlier [K. Koga, V. Holten, and B. Widom, J. Phys. Chem. B 119, 13391 (2015)] indicates that if B is asymptotically proportional to a power of σ, the exponent α must be equal to or greater than 6.

Solvation shell thermodynamics of extended hydrophobic solutes in mixed solvents

The ability of various cosolutes and cosolvents to enhance or quench solvent density fluctuations at solute–water interfaces has crucial implications on the conformational equilibrium of macromolecules such as polymers and proteins. Herein, we use an extended hydrophobic solute as a model system to study the effect of urea and methanol on the density fluctuations in the solute’s solvation shell and the resulting thermodynamics. On strengthening the solute–water/cosolute repulsive interaction, we observe distinct trends in the mutual affinities between various species in, and the thermodynamic properties of, the solvation shell. These trends strongly follow the respective trends in the preferential adsorption of urea and methanol: solute–water/cosolute repulsion strengthens, urea accumulation decreases, and methanol accumulation increases. Preferential accumulation of urea is found to quench the density fluctuations around the extended solute, leading to a decrease in the compressibility of the solvation shell. In contrast, methanol accumulation enhances the density fluctuations, leading to an increase in the compressibility. The mode of action of urea and methanol seems to be strongly coupled to their hydration behavior. The observations from this simple model is discussed in relation to urea driven swelling and methanol induced collapse of some well-known thermo-responsive polymers.

On the Nature of Guest Complexation in Water: Triggered Wetting-Water-Mediated Binding

The complexity of macromolecular surfaces means that there are still many open questions regarding how specific areas are solvated and how this might affect the complexation of guests. Contributing to the identification and classification of the different possible mechanisms of complexation events in aqueous solution, and as part of the recent SAMPL8 exercise, we report here on the synthesis and conformational properties of TEEtOA 2, a cavitand with conformationally flexible ethyl groups at its portal. Using a combination of ITC and NMR spectroscopy, we report the binding affinities of a series of carboxylates to 2 and compare it to a related cavitand TEMOA 1. Additionally, we report MD simulations revealing how the wetting of the pocket of 2 is controlled by the conformation of its rim ethyl groups and, correspondingly, a novel triggered wetting, guest complexation mechanism, whereby the approaching guest opens up the pocket of the host, inducing its wetting and ultimately allows the formation of a hydrated host-guest complex (H·G·H2O). A general classification of complexation mechanisms is also suggested.

Isothermal-isobaric algorithm to study the effects of rotational degrees of freedom-Benz water model

We have developed isothermal-isobaric algorithm for non-equilibrium Monte Carlo simulations. As first we have shown that the new method correctly predict density by comparing it to the density determined in canonical Monte Carlo simulations through the virial pressure. The new method was then used to study the effect of translational and rotational degrees of freedom on the structural and thermodynamic properties of the simple Mercedes-Benz water model. By holding one of the temperatures constant and varying the other one, we investigated how the position of the density maxima changes. We have observed that upon increase of rotational temperature the fluid become more Lennard-Jones like and the density maxima disappears.

Density Depletion and Enhanced Fluctuations in Water near Hydrophobic Solutes: Identifying the Underlying Physics

We investigate the origin of the density depletion and enhanced density fluctuations that occur in water in the vicinity of an extended hydrophobic solute. We argue that both phenomena are remnants of the critical drying surface phase transition that occurs at liquid-vapor coexistence in the macroscopic planar limit, i.e., as the solute radius R_{s}→∞. Focusing on the density profile ρ(r) and a sensitive spatial measure of fluctuations, the local compressibility profile χ(r), we develop a scaling theory which expresses the extent of the density depletion and enhancement in compressibility in terms of R_{s}, the strength of solute-water attraction ϵ_{s}, and the deviation from liquid-vapor coexistence δμ. Testing the predictions against results of classical density functional theory for a simple solvent and grand canonical Monte Carlo simulations of a popular water model, we find that the theory provides a firm physical basis for understanding how water behaves at a hydrophobe.

Evidence for Entropically Controlled Interfacial Hydration in Mesoporous Organosilicas

At aqueous interfaces, the distribution and dynamics of adsorbates are modulated by the behavior of interfacial water. Hydration of a hydrophobic surface can store entropy via the ordering of interfacial water, which contributes to the Gibbs energy of solute binding. However, there is little experimental evidence for the existence of such entropic reservoirs, and virtually no precedent for their rational design in systems involving extended interfaces. In this study, two series of mesoporous silicas were modified in distinct ways: (1) progressively deeper thermal dehydroxylation, via condensation of surface silanols, and (2) increasing incorporation of nonpolar organic linkers into the silica framework. Both approaches result in decreasing average surface polarity, manifested in a blue-shift in the fluorescence of an adsorbed dye. For the inorganic silicas, hydrogen-bonding of water becomes less extensive as the number of surface silanols decreases. Overhauser dynamic nuclear polarization (ODNP) relaxometry indicates enhanced surface water diffusivity, reflecting a loss of enthalpic hydration. In contrast, organosilicas show a monotonic decrease in surface water diffusivity with decreasing polarity, reflecting enhanced hydrophobic hydration. Molecular dynamics simulations predict increased tetrahedrality of interfacial water for the organosilicas, implying increased ordering near the nm-size organic domains (relative to inorganic silicas, which necessarily lack such domains). These findings validate the prediction that hydrophobic hydration at interfaces is controlled by the microscopic length scale of the hydrophobic regions. They further suggest that the hydration thermodynamics of structurally heterogeneous silica surfaces can be tuned to promote adsorption, which in turn tunes the selectivity in catalytic reactions.

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. II. Large Solvophovic Solutes

We use molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy as a function of temperature and pressure for hard-sphere solutes with diameters ranging from 4 to 36 Å in TIP4P/2005 and Jagla water-like solvents exhibiting unusual thermodynamics. An important piece of our discussion focuses on the nanometer-sized solutes, for which simulation results are found to be accounted for by the most basic classical thermodynamic treatment contemplating bulk and interfacial contributions to the solvation free energy. Thus, since water's liquid-vapor surface tension is only special inasmuch as it takes unusually large values, solvent's water-like unusual thermodynamics manifests through a term proportional to the pressure in the solvation free energy. As a result, such solvent's unusual thermodynamics is found to be relevant to the temperature and pressure dependence of the isochoric solvation energy and entropy as well as to the isothermal density derivative of the solvation free energy. This sharply contrasts with the findings of the first part of this series indicating that the solvation free energy of small hard spheres responds to temperature and pressure changes as solvent's density does, with such a contrasting picture embodying a "pressure-density dichotomy." As for the length-scale dependence, we find the zero nominal pressure and the solvent's temperature of the maximum density as singular conditions for cavity surface-area size scaling of large solutes to occur for all solvation quantities. We finally argue that the overall study undertaken in this series suggests that water's unusual thermodynamics may be relevant to the thermodynamic stability of clusters of solvophobic units in the temperature-pressure plane. Some comments on the role of solute-solvent attractive interactions are also depicted.

Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional

This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid-gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5 k_BT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes.

A Data-Driven Hydrophobicity Scale for Predicting Liquid-Liquid Phase Separation of Proteins

An accurate model for macroscale disordered assemblies of biological macromolecules such as those formed in so-called membraneless organelles would greatly assist in studying their structure, function, and dynamics. Recent evidence has suggested that liquid-liquid phase separation (LLPS) underlies the formation of membraneless organelles. While the general mechanism of exchange of macromolecule/water for macromolecule/macromolecule interactions is known to be the driving force for LLPS, the specific interactions involved are not well understood. One way that protein-water and protein-protein interactions have been understood historically is via hydrophobicity scales. However, these scales are typically optimized for describing these relative interactions in certain cases, such as protein folding or insertion of proteins into membranes. To better describe the relative interactions of proteins that undergo LLPS, we have developed a new, data-driven hydrophobicity scale. To determine the new scale, we used coarse-grained molecular dynamics simulations using the hydrophobicity scale coarse-grained model, which relates the interactions between amino acids to their hydrophobicity. Hydrophobicity values were determined via the force-balance method on a library of proteins that includes unfolded, intrinsically disordered, and phase-separating proteins (PSP). The resulting hydrophobicity scale can better predict whether a given protein will undergo LLPS at physiological conditions by using coarse-grained molecular dynamics simulations than existing hydrophobicity scales. This new scale confirms the importance of π-π interactions between amino acids as important drivers of LLPS. This new hydrophobicity scale provides a convenient and compact description of protein-protein interactions for proteins that undergo LLPS and could be used to develop new models to describe interactions between PSP and other components, such as nucleic acids.

Implicit Solvents for the Polarizable Atomic Multipole AMOEBA Force Field

Computational protein design, ab initio protein/RNA folding, and protein-ligand screening can be too computationally demanding for explicit treatment of solvent. For these applications, implicit solvent offers a compelling alternative, which we describe here for the polarizable atomic multipole AMOEBA force field based on three treatments of continuum electrostatics: numerical solutions to the nonlinear and linearized versions of the Poisson-Boltzmann equation (PBE), the domain-decomposition conductor-like screening model (ddCOSMO) approximation to the PBE, and the analytic generalized Kirkwood (GK) approximation. The continuum electrostatics models are combined with a nonpolar estimator based on novel cavitation and dispersion terms. Electrostatic model parameters are numerically optimized using a least-squares style target function based on a library of 103 small-molecule solvation free energy differences. Mean signed errors for the adaptive Poisson-Boltzmann solver (APBS), ddCOSMO, and GK models are 0.05, 0.00, and 0.00 kcal/mol, respectively, while the mean unsigned errors are 0.70, 0.63, and 0.58 kcal/mol, respectively. Validation of the electrostatic response of the resulting implicit solvents, which are available in the Tinker (or Tinker-HP), OpenMM, and Force Field X software packages, is based on comparisons to explicit solvent simulations for a series of proteins and nucleic acids. Overall, the emergence of performative implicit solvent models for polarizable force fields opens the door to their use for folding and design applications.

Cavitand Complexes in Aqueous Solution: Collaborative Experimental and Computational Studies of the Wetting, Assembly, and Function of Nanoscopic Bowls in Water

Water is the dominant liquid on Earth. Despite this, the main focus of supramolecular chemistry research has been on binding and assembly events in organic solvents. This arose because it is more straightforward to synthesize organic-media-soluble hosts and because of the relative simplicity of organic solvents compared to water. Nature, however, relies on water as a solvent, and spurred by this fact, supramolecular chemists have recently been making forays into the aqueous domain to understand water-mediated non-covalent interactions. These studies can benefit from the substantial understanding of the hydrophobic effect and electrostatic interactions developed by physical chemists. Nearly 20 years ago, the Gibb group first synthesized a class of water-soluble host molecules, the deep-cavity cavitands, that possess non-polar pockets that readily bind non-polar moieties in aqueous solution and are capable of assembling into a wide range of complexes with distinct stoichiometries. As such, these amphipathic host species are ideal platforms for studying the role of negatively curved features on guest complexation and the structural requirements for guided assembly processes driven by the hydrophobic effect. Here we review the collaborative experimental and computational investigations between Gibb and Ashbaugh over the past 10 years exploring questions including the following: How does water wet/solvate the non-polar surfaces of non-polar pockets? How does this wetting control the binding of non-polar guests? How does wetting affect the binding of anionic species? How does the nature and size of a guest size impact the assembly of cavitand hosts into multimeric capsular complexes? What are the conformational motifs of guests packed within the confines of capsular complexes? How might the electrostatic environment engendered by hosts impact the properties and reactivity of internalized guests?

Pressure Induced Wetting and Dewetting of the Nonpolar Pocket of Deep-Cavity Cavitands in Water

Hydrophobic interactions drive the binding of nonpolar ligands to the oily pockets of proteins and supramolecular species in aqueous solution. As such, the wetting of host pockets is expected to play a critical role in determining the thermodynamics of guest binding. Here we use molecular simulations to examine the impact of pressure on the wetting and dewetting of the nonpolar pockets of a series of deep-cavity cavitands in water. The portals to the cavitand pockets are functionalized with both nonpolar (methyl) and polar (hydroxyl) groups oriented pointing either upward or inward toward the pocket. We find wetting of the pocket is favored by the hydroxyl groups and dewetting is favored by the methyl groups. The distribution of waters in the pocket is found to exhibit a two-state-like equilibrium between wet and dry states with a free energy barrier between the two states. Moreover, we demonstrate that the pocket hydration of the cavitands can be collapsed onto a unified adsorption isotherm by assuming the effective pressures within each cavitand pocket differ by a shift pressure that depends on the chemical identity and number of functional groups placed about the portal. These observations support the development of a two-state capillary evaporation model that accurately describes the equilibrium between states and naturally gives rise to the effective shift pressures observed from simulation. This work demonstrates that the hydration of host pockets can be tuned following simple design rules that in turn are expected to impact the thermodynamics of guest complexation.

Spontaneous drying of non-polar deep-cavity cavitand pockets in aqueous solution

There are many open questions regarding the hydration of solvent-exposed non-polar tracts and pockets in proteins. Although water is predicted to de-wet purely repulsive surfaces and evacuate crevices, the extent of de-wetting is unclear when ubiquitous van der Waals interactions are in play. The structural simplicity of synthetic supramolecular hosts imbues them with considerable potential to address this issue. To this end, here we detail a combination of densimetry and molecular dynamics simulations of three cavitands, coupled with calorimetric studies of their complexes with short-chain carboxylates. Our results reveal the range of wettability possible within the ostensibly identical cavitand pockets-which differ only in the presence and/or position of the methyl groups that encircle the portal to their non-polar pockets. The results demonstrate the ability of macrocycles to template water cavitation within their binding sites and show how the orientation of methyl groups can trigger the drying of non-polar pockets in liquid water, which suggests new avenues to control guest complexation.

Proximal charge effects on guest binding to a non-polar pocket

Science still does not have the ability to accurately predict the affinity that ligands have for proteins. In an attempt to address this, the Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) series of blind predictive challenges is a community-wide exercise aimed at advancing computational techniques as standard predictive tools in rational drug design. In each cycle, a range of biologically relevant systems of different levels of complexity are selected to test the latest modeling methods. As part of this on-going exercise, and as a step towards understanding the important factors in context dependent guest binding, we challenged the computational community to determine the affinity of a series of negatively and positively charged guests to two constitutionally isomeric cavitand hosts: octa-acid 1, and exo-octa acid 2. Our affinity determinations, combined with molecular dynamics simulations, reveal asymmetries in affinities between host-guest pairs that cannot alone be explained by simple coulombic interactions, but also point to the importance of host-water interactions. Our work reveals the key facets of molecular recognition in water, emphasizes where improvements need to be made in modelling, and shed light on the complex problem of ligand-protein binding in the aqueous realm.

Water Structure and Properties at Hydrophilic and Hydrophobic Surfaces

The properties of water on both molecular and macroscopic surfaces critically influence a wide range of physical behaviors, with applications spanning from membrane science to catalysis to protein engineering. Yet, our current understanding of water interfacing molecular and material surfaces is incomplete, in part because measurement of water structure and molecular-scale properties challenges even the most advanced experimental characterization techniques and computational approaches. This review highlights progress in the ongoing development of tools working to answer fundamental questions on the principles that govern the interactions between water and surfaces. One outstanding and critical question is what universal molecular signatures capture the hydrophobicity of different surfaces in an operationally meaningful way, since traditional macroscopic hydrophobicity measures like contact angles fail to capture even basic properties of molecular or extended surfaces with any heterogeneity at the nanometer length scale. Resolving this grand challenge will require close interactions between state-of-the-art experiments, simulations, and theory, spanning research groups and using agreed-upon model systems, to synthesize an integrated knowledge of solvation water structure, dynamics, and thermodynamics.

Bridging solvent molecules mediate RNase A - Ligand binding

Due to its high catalytic activity and readily available supply, ribonuclease A (RNase A) has become a pivotal enzyme in the history of protein science. Moreover, this great interest has carried over to computational chemistry and molecular dynamics, where RNase A has become a model system for various types of studies, all the while being an important drug design target in its own right. Here, we present a detailed molecular dynamics study of RNase–ligand binding involving 22 compounds, spanning nearly five orders of magnitude in affinity, and totaling 8.8 μs of sampling with the standard Amber parameters and an additional 8.8 μs of sampling with a modified potential. We show that short-lived, solvent-mediated bridging interactions are crucial to RNase–ligand binding. We characterize the behavior of bridging solvent molecules, uncovering a power-law dependence between the lifetime of a solvent bridge and the probability of its occurrence. We also demonstrate that from an energetic perspective, bridging solvent in RNase A–ligand binding behaves like part of the enzyme, rather than the ligands. Moreover, we describe an automated pipeline for the detection and processing of bridging interactions, and offer an independent assessment of the performance of the state-of-the-art fixed-charge force fields. Thus, our work has broad implications for drug design and computational chemistry in general.

Self-assembly in amphiphilic macromolecules with solvent exposed hydrophobic moieties

Self-assembly by amphiphilic molecules with solvent exposed hydrophobic groups are relevant in biomolecular systems as well as in technological applications. Here we study such self-assembly in these systems using a model system of spherical particles having charge at core but solvent repelling surface, using Monte-Carlo simulations and mean field treatment. We find that solvophobicity mediated attraction leads aggregation, while electrostatic repulsions control stability of finite clusters. The aggregation threshold relates the parameters of two interactions through an algebraic dependence. The study also qualitatively explains experimental observations on aggregation of misfolded proteins and can be useful guide to tune stability of nm sized self-assembly in systems with exposed hydrophobic groups.

Decoding signatures of structure, bulk thermodynamics, and solvation in three-body angle distributions of rigid water models

A tetrahedral structure resulting from hydrogen bonding is a hallmark of liquid water and plays a significant role in determining its unique thermophysical properties. This water feature has helped understand anomalous properties and physically interpret and model hydrophobic solvation thermodynamics. Tetrahedrality is well described by the geometric relationship of any central water molecule with two of its nearest neighbors in the first coordination shell, as defined by the corresponding "three-body" angle. While order parameters and even full water models have been developed using specific or average features of the three-body angle distribution, here we examine the distribution holistically, tracking its response to changes in temperature, density, and the presence of model solutes. Surprisingly, we find that the three-body distribution responds by varying primarily along a single degree of freedom, suggesting a remarkably simplified view of water structure. We characterize three-body angle distributions across temperature and density space and identify principal components of the variations with state conditions. We show that these principal components embed physical significance and trace out transitions between tetrahedral and simple-fluid-like behavior. Moreover, we find that the ways three-body angles vary within the hydration shells of model colloids of different types and sizes are nearly identical to the variations seen in bulk water across density and temperature. Importantly, through the principal directions of these variations, we find that perturbations to the hydration-water distributions well predict the thermodynamics associated with colloid solvation, in particular, the relative entropy of this process that captures indirect, solvent-mediated contributions to the hydration free energy.

Molecular Modeling of Surfactant Micellization Using Solvent-Accessible Surface Area

We report a new implicit solvent simulation model for studying the self-assembly of surfactants, where the hydrophobic interactions were captured by calculating the relative changes of the solvent-accessible surface area (SASA) of the hydrophobic domains. Using histogram-reweighting grand canonical Monte Carlo simulations, we demonstrate that this approach allows us to match both the experimental critical micelle concentrations (cmc) and micellar aggregation numbers simultaneously with a single phenomenological surface tension γ_SASA for the poly(oxyethylene) monoalkyl ether (C _mE _n) surfactants in aqueous solutions. Excellent transferability is observed: the same model can accurately predict the experimental cmc and aggregation numbers for the C _mE _n surfactants with the alkyl lengths m between 6 and 12 and the poly(oxyethylene) lengths n between 1 and 9. The SASA-based implicit solvent model put forward in this work is general and may be applied to study more complex amphiphilic systems such as surfactants with branched alkyl chains or surfactant-hydrocarbon mixtures.

Short-range combined water model

The short-range combined water model (SRCW model) for the calculation of the hydration free energy of the non-polar solutes is presented. A mixed explicit/implicit representation of the solvent is used in the model. A thermodynamic basis for the boundary potential between explicit and implicit parts of the simulation area is derived. A simple functional form for the boundary potential minimizing the water density fluctuations in the explicit part is found. Hydration free energies of the model solutes are calculated in the frame of the developed model. Obtained values are in the good agreement with results of the Monte Carlo simulation using the periodic boundary conditions.

Direct Measurement of Length Scale Dependence of the Hydrophobic Free Energy of a Single Collapsed Polymer Nanosphere

The physics underlying hydrophobicity at macroscopic and microscopic levels is fundamentally distinct. However, experimentally quantifying the length scale dependence of hydrophobicity is challenging. Here we show that the size-dependent hydrophobic free energy of a collapsed polymer nanosphere can be continuously monitored from its single-molecule force-extension curve using a novel theoretical framework. The hydrophobic free energy shows a change from cubic to square dependence of the radius of the polymer nanosphere at a radius of ∼1  nm-this is consistent with Lum-Chandler-Weeks theory and simulations. We can also observe a large variation of the hydrophobic free energy of each polymer nanosphere implying the heterogeneity of the self-assembled structures and/or the fluctuation of the water-polymer interface. We expect that our approach can be used to address many fundamental questions about hydrophobic hydration, which are otherwise inaccessible by ensemble measurements.

The Kinetics, Thermodynamics and Mechanisms of Short Aromatic Peptide Self-Assembly

The self-assembly of short aromatic peptides and peptide derivatives into a variety of different nano- and microstructures (fibrillar gels, crystals, spheres, plates) is a promising route toward the creation of bio-compatible materials with often unexpected and useful properties. Furthermore, such simple self-assembling systems have been proposed as model systems for the self-assembly of longer peptides, a process that can be linked to biological function and malfunction. Much effort has been made in the last 15 years to explore the space of peptide sequences, chemical modifications and solvent conditions in order to maximise the diversity of assembly morphologies and properties. However, quantitative studies of the corresponding mechanisms of, and driving forces for, peptide self-assembly have remained relatively scarce until recently. In this chapter we review the current state of understanding of the thermodynamic driving forces and self-assembly mechanisms of short aromatic peptides into supramolecular structures. We will focus on experimental studies of the assembly process and our perspective will be centered around diphenylalanine (FF), a key motif of the amyloid β sequence and a paradigmatic self-assembly building block. Our main focus is the basic physical chemistry and key structural aspects of such systems, and we will also compare the mechanism of dipeptide aggregation with that of longer peptide sequences into amyloid fibrils, with discussion on how these mechanisms may be revealed through detailed analysis of growth kinetics, thermodynamics and other fundamental properties of the aggregation process.

Interfacial structural crossover and hydration thermodynamics of charged C60 in water

Classical molecular dynamics simulations of the hydration thermodynamics, structure, and dynamics of water in hydration shells of charged buckminsterfullerenes are presented in this study. Charging of fullerenes leads to a structural transition in the hydration shell, accompanied by creation of a significant population of dangling O-H bonds pointing toward the solute. In contrast to the well accepted structure-function paradigm, this interfacial structural transition causes nearly no effect on either the dynamics of hydration water or on the solvation thermodynamics. Linear response to the solute charge is maintained despite significant structural changes in the hydration shell, and solvation thermodynamic potentials are nearly insensitive to the altering structure. Only solvation heat capacities, which are higher thermodynamic derivatives of the solvation free energy, indicate some sensitivity to the local hydration structure. We have separated the solvation thermodynamic potentials into direct solute-solvent interactions and restructuring of the hydration shell and analyzed the relative contributions of electrostatic and nonpolar interactions to the solvation thermodynamics.

Study of distance dependence of hydrophobic force between two graphene-like walls and a signature of pressure induced structure formation in the confined water

We examine the separation distance dependence of the hydrophobic force by systematically varying the distance (d) between two walls. The hydrophobic force exhibits a distance mediated crossover from a liquid-like to a gas-like behavior at around d ∼ 12 Å for 1 atm pressure. The distance dependence can be fitted to a bi-exponential form, with the longer distance part displaying a correlation length of 20 Å. In addition, the crossover is found to be accompanied by a divergent-like growth of the local relative number fluctuation of the water molecules confined between the two surfaces. Furthermore, at a fixed separation (d = 20 Å), we observe a pressure induced structural modification of confined water at high pressure. The confined water is found to form an ordered structure at high pressure (10 000 atm) and room temperature, in agreement with the experimental study [G. Algara-Siller et al. Nature 519(7544), 443 (2015)].

Alchemical free energy calculations and umbrella sampling with local molecular field theory

Understanding the thermodynamic driving forces underlying any chemical process requires a description of the underlying free energy surface. However, computation of free energies is difficult, often requiring advanced sampling techniques. Moreover, these computations can be further complicated by the evaluation of any long-ranged interactions in the system of interest, such as Coulomb interactions in charged and polar media. Local molecular field theory is a promising approach to avoid many of the conceptual and computational difficulties associated with long-ranged interactions. We present frameworks for performing alchemical free energy calculations and non-Boltzmann sampling with local molecular field theory. We demonstrate that local molecular field theory can be used to perform these free energy calculations with accuracy comparable to traditional methodologies while eliminating the need for explicit treatment of long-ranged interactions in simulations.

Physico-chemical properties of aqueous drug solutions: From the basic thermodynamics to the advanced experimental and simulation results

The physical chemical properties of aqueous solutions of model compounds are illustrated in relation to hydration and solubility issues by using three perspectives: thermodynamic, spectroscopic and molecular dynamics simulations. The thermodynamic survey of the fundamental backgrounds of concentration dependence and experimental solubility results show some peculiar behavior of aqueous solutions with several types of similar solutes. Secondly, the use of a variety of experimental spectroscopic devices, operating under different experimental conditions of dimension and frequency, has produced a large amount of structural and dynamic data on aqueous solutions showing the richness of the information produced, depending on where and how the experiment is carried out. Finally, the use of molecular dynamics computational work is presented to highlight how the different types of solute functional groups and surface topologies organize adjacent water molecules differently. The highly valuable contribution of computer simulation studies in providing molecular explanations for experimental deductions, either of a thermodynamic or spectroscopic nature, is shown to have changed the current knowledge of many aqueous solution processes. While this paper is intended to provide a collective view on the latest literature results, still the presentation aims at a tutorial explanation of the potentials of the three methodologies in the field of aqueous solutions of pharmaceutical molecules.