Temperature and length scale dependence of hydrophobic effects and their possible implications for protein folding

Biomolecular Phase Separation: From Molecular Driving Forces to Macroscopic Properties

Biological phase separation is known to be important for cellular organization, which has recently been extended to a new class of biomolecules that form liquid-like droplets coexisting with the surrounding cellular or extracellular environment. These droplets are termed membraneless organelles, as they lack a dividing lipid membrane, and are formed through liquid-liquid phase separation (LLPS). Elucidating the molecular determinants of phase separation is a critical challenge for the field, as we are still at the early stages of understanding how cells may promote and regulate functions that are driven by LLPS. In this review, we discuss the role that disorder, perturbations to molecular interactions resulting from sequence, posttranslational modifications, and various regulatory stimuli play on protein LLPS, with a particular focus on insights that may be obtained from simulation and theory. We finally discuss how these molecular driving forces alter multicomponent phase separation and selectivity.

Length-scale dependence of protein hydration-shell density

Here we present a computational approach based on molecular dynamics (MD) simulation to study the dependence of the protein hydration-shell density on the size of the protein molecule. The hydration-shell density of eighteen different proteins, differing in size, shape and function (eight of them are antifreeze proteins), is calculated. The results obtained show that an increase in the hydration-shell density, relative to that of the bulk, is observed (in the range of 4-14%) for all studied proteins and that this increment strongly correlates with the protein size. In particular, a decrease in the density increment is observed for decreasing protein size. A simple model is proposed in which the basic idea is to approximate the protein molecule as an effective ellipsoid and to partition the relevant parameters, i.e. the solvent-accessible volume and the corresponding solvent density, into two regions: inside and outside the effective protein ellipsoid. It is found that, within the model developed here, almost all of the hydration-density increase is located inside the protein ellipsoid, basically corresponding to pockets within, or at the surface of the protein molecule. The observed decrease in the density increment is caused by the protein size only and no difference is found between antifreeze and non-antifreeze proteins.

Environment-dependent single-chain mechanics of synthetic polymers and biomacromolecules by atomic force microscopy-based single-molecule force spectroscopy and the implications for advanced polymer materials

"The Tao begets the One. One begets all things of the world." This quote from Tao Te Ching is still inspiring for scientists in chemistry and materials science: The "One" can refer to a single molecule. A macroscopic material is composed of numerous molecules. Although the relationship between the properties of the single molecule and macroscopic material is not well understood yet, it is expected that a deeper understanding of the single-chain mechanics of macromolecules will certainly facilitate the development of materials science. Atomic force microscopy-based single-molecule force spectroscopy (AFM-SMFS) has been exploited extensively as a powerful tool to study the single-chain behaviors of macromolecules. In this review, we summarize the recent advances in the emerging field of environment-dependent single-chain mechanics of synthetic polymers and biomacromolecules by means of AFM-SMFS. First, the single-chain inherent elasticities of several typical linear macromolecules are introduced, which are also confirmed by one of three polymer models with theoretical elasticities of the corresponding macromolecules obtained from quantum mechanical (QM) calculations. Then, the effects of the external environments on the single-chain mechanics of synthetic polymers and biomacromolecules are reviewed. Finally, the impacts of single-chain mechanics of macromolecules on the development of polymer science especially polymer materials are illustrated.

A thermophilic phage uses a small terminase protein with a fixed helix-turn-helix geometry

Tailed bacteriophages use a DNA-packaging motor to encapsulate their genome during viral particle assembly. The small terminase (TerS) component of this DNA-packaging machinery acts as a molecular matchmaker that recognizes both the viral genome and the main motor component, the large terminase (TerL). However, how TerS binds DNA and the TerL protein remains unclear. Here we identified gp83 of the thermophilic bacteriophage P74-26 as the TerS protein. We found that TerS^P76-26 oligomerizes into a nonamer that binds DNA, stimulates TerL ATPase activity, and inhibits TerL nuclease activity. A cryo-EM structure of TerS^P76-26 revealed that it forms a ring with a wide central pore and radially arrayed helix-turn-helix domains. The structure further showed that these helix-turn-helix domains, which are thought to bind DNA by wrapping the double helix around the ring, are rigidly held in an orientation distinct from that seen in other TerS proteins. This rigid arrangement of the putative DNA-binding domain imposed strong constraints on how TerS^P76-26 can bind DNA. Finally, the TerS^P76-26 structure lacked the conserved C-terminal β-barrel domain used by other TerS proteins for binding TerL. This suggests that a well-ordered C-terminal β-barrel domain is not required for TerS^P76-26 to carry out its matchmaking function. Our work highlights a thermophilic system for studying the role of small terminase proteins in viral maturation and presents the structure of TerS^P76-26, revealing key differences between this thermophilic phage and its mesophilic counterparts.

On the Nonaggregation of Normal Adult Hemoglobin and the Aggregation of Sickle Cell Hemoglobin

Sickle cell disease is a genetic disorder associated with a single mutation (Glu-β6 → Val-β6) in the β chains of hemoglobin, causing the polymerization of deoxygenated sickle cell hemoglobin (deoxy-HbS). The deoxy-HbS binding free energy was recently studied through molecular simulations, and a value of -14 ± 1 kcal mol^-1 was found. Here, we studied the binding free energy of normal adult hemoglobin (deoxy-HbA), which does not polymerize at normal physiological conditions, with the aim of elucidating the importance of the presence of Val-β6 and of the absence of Glu-β6 on the aggregation of deoxy-HbS. A binding free energy of -4.4 ± 0.5 kcal mol^-1 was found from a one-dimensional potential of mean force. Hydrophobic interactions are shown to represent less than 20% of the interactions in the contact interface, and despite similarly strong hydrogen-bonded ion pairs (i.e., salt bridges) and water bridged electrostatic interactions are found for deoxy-HbA and deoxy-HbS, a large repulsive potential energy is associated with Glu-β6, whereas a mild attractive potential energy is connected with Val-β6. Interestingly, Asp-β73 switches from forming a major electrostatic repulsive pair with Glu-β6 in deoxy-HbA, to forming a major attractive residue pair with Val-β6 in deoxy-HbS, consistent with the view that damping of electrostatic repulsions involving Glu-β6, namely, those associated with Asp-β73, could be responsible for the polymerization of deoxy-HbA at high potassium phosphate concentrations. Solvation analysis shows that functional groups forming salt bridges and water bridged interactions preserve a nearly intact first hydration sphere, avoiding a complete dewetting free energy penalty. These results support the view that the absence of Glu-β6 is more important than the presence of Val-β6, and that although hydrophobic effects, associated with the Val-β6 dehydration and interaction with the hydrophobic pocket in the neighbor tetramer, are important, electrostatic interactions are dominant, opposite to a picture where HbS association is driven by hydrophobic interactions.

Principles for enhancing virus capsid capacity and stability from a thermophilic virus capsid structure

The capsids of double-stranded DNA viruses protect the viral genome from the harsh extracellular environment, while maintaining stability against the high internal pressure of packaged DNA. To elucidate how capsids maintain stability in an extreme environment, we use cryoelectron microscopy to determine the capsid structure of thermostable phage P74-26 to 2.8-Å resolution. We find P74-26 capsids exhibit an overall architecture very similar to those of other tailed bacteriophages, allowing us to directly compare structures to derive the structural basis for enhanced stability. Our structure reveals lasso-like interactions that appear to function like catch bonds. This architecture allows the capsid to expand during genome packaging, yet maintain structural stability. The P74-26 capsid has T = 7 geometry despite being twice as large as mesophilic homologs. Capsid capacity is increased with a larger, flatter major capsid protein. Given these results, we predict decreased icosahedral complexity (i.e. T ≤ 7) leads to a more stable capsid assembly.

Viral capsids need to protect the genome against harsh environmental conditions and cope with high internal pressure from the packaged genome. Here, the authors determine the structure of the thermostable phage P74-26 capsid at 2.8-Å resolution and identify features underlying enhanced capsid capacity and structural stability.

Recovering superhydrophobicity in nanoscale and macroscale surface textures

Here, we investigate the complete drying of hydrophobic cavities in order to elucidate the dependence of drying on the size, the geometry, and the degree of hydrophobicity of the confinement. Two complementary theoretical approaches are adopted: a macroscopic one based on classical capillarity and a microscopic classical density functional theory. This combination allows us to pinpoint unique drying mechanisms at the nanoscale and to clearly differentiate them from the mechanisms operational at the macroscale. Nanoscale hydrophobic cavities allow the thermodynamic destabilization of the confined liquid phase over an unexpectedly broad range of conditions, including pressures as large as 10 MPa and contact angles close to 90°. On the other hand, for cavities on the micron scale, such destabilization occurs only for much larger contact angles and close to liquid-vapor coexistence. These scale-dependent drying mechanisms are used to propose design criteria for hierarchical superhydrophobic surfaces capable of spontaneous self-recovery over a broad range of operating conditions. In particular, we detail the requirements under which it is possible to realize perpetual superhydrophobicity at positive pressures on surfaces with micron-sized textures by exploiting drying, facilitated by nanoscale coatings. Concerning the issue of superhydrophobicity, these findings indicate a promising direction both for surface fabrication and for the experimental characterization of perpetual surperhydrophobicity. From a more basic perspective, the present results have an echo on a wealth of biological problems in which hydrophobic confinement induces drying, such as in protein folding, molecular recognition, and hydrophobic gating.

Spontaneously Forming Dendritic Voids in Liquid Water Can Host Small Polymers

Some liquids are characterized by the presence of large voids with dendritic shapes and for this reason are dubbed transiently porous. By using a battery of data analysis tools, we demonstrate that liquid water and methane are both characterized by transient porosity. We show that the thermodynamics of porosity is distinct from that associated with cavitation á la classical nucleation theory. The shapes of dendritic voids in both liquids with very different chemistries resemble those of small polymers. We further show, using free energy calculations, that the cost of solvating small hydrophobic polymers in water is consistent with the work associated with creating dendritic voids. The entropic and enthalpic contributions associated with hosting these polymers can thus be rationalized by the thermodynamics of fluctuations in bulk water.

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.

Structural features of high-local-density water molecules: Insights from structure indicators based on the translational order between the first two molecular shells

The two-liquids scenario for liquid water assumes the existence of two competing preferential local molecular structural states characterized by either low or high local density. While the former is expected to present good local order thus involving privileged structures, the latter is usually regarded as conforming a high-entropy unstructured state. A main difference in the local arrangement of such "classes" of water molecules can be inferred from the degree of translational order between the first and second molecular shells. This is so, since the low-local-density molecules present a clear gap between the first two shells while in the case of the high-local-density ones, one or more molecules from the second shell have collapsed toward the first one, thus populating the intershell region. Some structural indicators, like the widely employed local structure index and the recently introduced ζ index, have been devised precisely on the basis of this observation, being successful in detecting well-structured low-local-density molecules. However, the nature of the high-local-density state has been mainly disregarded over the years. In this work we employ molecular dynamics simulations for two water models (the extended simple point charge model and the five-site model) at the liquid and supercooled regimes combined with the inherent dynamics approach (energy minimizations of the instantaneous configurations) in order to both rationalize the detailed structural and topological information that these indicators provide and to advance in our understanding of the high-density state.

Temperature-Controlled Liquid-Liquid Phase Separation of Disordered Proteins

The liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) is a commonly observed phenomenon within the cell, and such condensates are also highly attractive for applications in biomaterials and drug delivery. A better understanding of the sequence-dependent thermoresponsive behavior is of immense interest as it will aid in the design of protein sequences with desirable properties and in the understanding of cellular response to heat stress. In this work, we use a transferable coarse-grained model to directly probe the sequence-dependent thermoresponsive phase behavior of IDPs. To achieve this goal, we develop a unique knowledge-based amino acid potential that accounts for the temperature-dependent effects on solvent-mediated interactions for different types of amino acids. Remarkably, we are able to distinguish between more than 35 IDPs with upper or lower critical solution temperatures at experimental conditions, thus providing direct evidence that incorporating the temperature-dependent solvent-mediated interactions to IDP assemblies can capture the difference in the shape of the resulting phase diagrams. Given the success of the model in predicting experimental behavior, we use it as a high-throughput screening framework to scan through millions of disordered sequences to characterize the composition dependence of protein phase separation.

Molecular Order Affects Interfacial Water Structure and Temperature-Dependent Hydrophobic Interactions between Nonpolar Self-Assembled Monolayers

Understanding how material properties affect hydrophobic interactions-the water-mediated interactions that drive the association of nonpolar materials-is vital to the design of materials in contact with water. Conventionally, the magnitude of the hydrophobic interactions between extended interfaces is attributed to interfacial chemical properties, such as the amount of nonpolar solvent-exposed surface area. However, recent experiments have demonstrated that the hydrophobic interactions between uniformly nonpolar self-assembled monolayers (SAMs) also depend on molecular-level SAM order. In this work, we use atomistic molecular dynamics simulations to investigate the relationship between SAM order, water structure, and hydrophobic interactions to explain these experimental observations. The SAM-SAM hydrophobic interactions calculated from the simulations increase in magnitude as SAM order increases, matching experimental observations. We explain this trend by showing that the molecular-level order of the SAM impacts the nanoscale structure of interfacial water molecules, leading to an increase in water structure near disordered SAMs. These findings are consistent with a decrease in the solvation entropy of disordered SAMs, which is confirmed by measuring the temperature dependence of hydrophobic interactions using both simulations and experiments. This study elucidates how hydrophobic interactions can be influenced by an interfacial physical property, which may guide the design of synthetic materials with fine-tuned interfacial hydrophobicity.

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.

Influence of glycerol on the cooling effect of pair hydrophobicity in water: relevance to proteins’ stabilization at low temperature

Glycerol reduces the cooling effect of pair hydrophobicity (reduction of hydrophobicity with decreasing temperature) in water.

Fast Pairwise Approximation of Solvent Accessible Surface Area for Implicit Solvent Simulations of Proteins on CPUs and GPUs

We propose a pairwise and readily parallelizable SASA-based nonpolar solvation approach for protein simulations, inspired by our previous pairwise GB polar solvation model development. In this work, we developed a novel function to estimate the atomic and molecular SASAs of proteins, which results in comparable accuracy as the LCPO algorithm in reproducing numerical icosahedral-based SASA values. Implemented in Amber software and tested on consumer GPUs, our pwSASA method reasonably reproduces LCPO simulation results, but accelerates MD simulations up to 30 times compared to the LCPO implementation, which is greatly desirable for protein simulations facing sampling challenges. The value of incorporating the nonpolar term in implicit solvent simulations is explored on a peptide fragment containing the hydrophobic core of HP36 and evaluating thermal stability profiles of four small proteins.

How do glycerol and dimethyl sulphoxide affect local tetrahedral structure of water around a nonpolar solute at low temperature? Importance of preferential interaction

Glycerol and dimethyl sulphoxide (DMSO) have vital roles in cryoprotection of living cells, tissues, etc. The above action has been directly linked with disruption of hydrogen (H-) bond structure and dynamics of water by these cosolvents at bulk region and around various complex units, such as peptide, amino acid, protein, and lipid membrane. However, the disruption of the local structure of the water solvent around a purely hydrophobic solute is still not studied extensively. The latter is also important in the context of stabilization of protein from cold denaturation. Through all-atom molecular dynamics simulation, we have investigated the comparative effect of glycerol and DMSO on the orientational order of water around a nonpolar solute at -5 °C. A steady reduction of the tetrahedral order of water is observed at bulk (>10 Å distance from the solute) and solute interface (<5.5 Å distance from the solute) with increasing the cosolvent concentration. Contrasting roles of glycerol and DMSO have been evidenced. While DMSO affects the H-bond structure of the interfacial water more than that of the bulk water, glycerol affects the water structure almost uniformly at all regions around the solute. Furthermore, while glycerol helps to retain water molecules at the interface, DMSO significantly reduces the water content in that region. We have put forward a plausible mechanism for these contrasting roles of these cosolvents. The solute-cosolvent hydrophobic-interaction-induced orientational alignment of an interfacial cosolvent molecule determines whether the involvement of the cosolvent molecules in H-bonding with solvent water in the interface is akin to the bulk region or not.

The spatial range of protein hydration

Proteins interact with their aqueous surroundings, thereby modifying the physical properties of the solvent. The extent of this perturbation has been investigated by numerous methods in the past half-century, but a consensus has still not emerged regarding the spatial range of the perturbation. To a large extent, the disparate views found in the current literature can be traced to the lack of a rigorous definition of the perturbation range. Stating that a particular solvent property differs from its bulk value at a certain distance from the protein is not particularly helpful since such findings depend on the sensitivity and precision of the technique used to probe the system. What is needed is a well-defined decay length, an intrinsic property of the protein in a dilute aqueous solution, that specifies the length scale on which a given physical property approaches its bulk-water value. Based on molecular dynamics simulations of four small globular proteins, we present such an analysis of the structural and dynamic properties of the hydrogen-bonded solvent network. The results demonstrate unequivocally that the solvent perturbation is short-ranged, with all investigated properties having exponential decay lengths of less than one hydration shell. The short range of the perturbation is a consequence of the high energy density of bulk water, rendering this solvent highly resistant to structural perturbations. The electric field from the protein, which under certain conditions can be long-ranged, induces a weak alignment of water dipoles, which, however, is merely the linear dielectric response of bulk water and, therefore, should not be thought of as a structural perturbation. By decomposing the first hydration shell into polarity-based subsets, we find that the hydration structure of the nonpolar parts of the protein surface is similar to that of small nonpolar solutes. For all four examined proteins, the mean number of water-water hydrogen bonds in the nonpolar subset is within 1% of the value in bulk water, suggesting that the fragmentation and topography of the nonpolar protein-water interface has evolved to minimize the propensity for protein aggregation by reducing the unfavorable free energy of hydrophobic hydration.

Temperature-Dependent Hydrophobic Crossover Length Scale and Water Tetrahedral Order

Experimental Raman multivariate curve resolution and molecular dynamics simulations are performed to demonstrate that the vibrational frequency and tetrahedrality of water molecules in the hydration-shells of short-chain alcohols differ from those of pure water and undergo a crossover above 100 °C (at 30 MPa) to a structure that is less tetrahedral than pure water. Our results demonstrate that the associated crossover length scale decreases with increasing temperature, suggesting that there is a fundamental connection between the spectroscopically observed crossover and that predicted to take place around idealized purely repulsive solutes dissolved in water, although the water structure changes in the hydration-shells of alcohols are far smaller than those associated with an idealized "dewetting" transition.

Mapping Hydration Water around Alcohol Chains by THz Calorimetry

THz spectroscopy was used to probe changes that occur in the dynamics of the hydrogen bond network upon solvation of alcohol chains. The THz spectra can be decomposed into the spectrum of bulk water, tetrahedral hydration water, and more disordered (or interstitial) hydration water. The tetrahedrally ordered hydration water exhibits a band at 195 cm⁻¹ and is localized around the hydrophobic moiety of the alcohol. The interstitial component yields a band at 164 cm⁻¹ which is associated with hydration water in the first hydration shell. These temperature‐dependent changes in the low‐frequency spectrum of solvated alcohol chains can be correlated with changes of heat capacity, entropy, and free energy upon solvation. Surprisingly, not the tetrahedrally ordered component but the interstitial hydration water is found to be mainly responsible for the temperature‐dependent change in ΔC_p and ΔG. The solute‐specific offset in free energy is attributed to void formation and scales linearly with the chain length.

Influence of Order within Nonpolar Monolayers on Hydrophobic Interactions

We report an experimental investigation of the influence of molecular-level order (crystallinity) within nonpolar monolayers on hydrophobic interactions. The measurements were performed using gold film-supported monolayers formed from alkanethiols (CH₃(CH₂)_nSH, with n ranging from 3 to 17), which we confirmed by using polarization-modulation infrared reflection-adsorption spectroscopy to exhibit chain-length-dependent order (methylene peak moves from 2926 to 2919 cm^-1, corresponding to a transition from liquid- to quasi-crystalline-like order) in the absence of substantial changes in chain density (constant methyl peak intensity). By using monolayer-covered surfaces immersed in either aqueous triethanolamine (TEA, 10 mM, pH 7.0) or pure methanol, we quantified hydrophobic and van der Waals contributions to adhesive interactions between identical pairs of surfaces (measured using an atomic force microscope) as a function of the length and order of the aliphatic chains within the monolayers. In particular, we measured pull-off forces arising from hydrophobic adhesion to increase in a nonlinear manner with chain length (abrupt increase between n = 5 and 6 from 2.1 ± 0.3 to 14.1 ± 0.7 nN) and to correlate closely with a transition from a liquid-like to crystalline-like monolayer phase. In contrast, adhesion in methanol increased gradually with chain length from 0.3 ± 0.1 to 3.2 ± 0.3 nN for n = 3 to 7 and then did not change further with an increase in chain length. These results lead to the hypothesis that order within nonpolar monolayers influences hydrophobic interactions. Additional support for this hypothesis was obtained from measurements reported in this paper using long-chain alkanethiols (ordered) and alkenethiols (disordered). The results are placed into the context of recent spectroscopic studies of hydrogen bonding of water at nonpolar monolayers. Overall, our study provides new insight into factors that influence hydrophobic interactions at nonpolar monolayers.

Temperature and pressure dependence of the interfacial free energy against a hard surface in contact with water and decane

Theoretical descriptions of molecular-scale solvation frequently invoke contributions proportional to the solvent exposed area, under the tacit expectation that those contributions are tied to a surface tension for macroscopic surfaces. Here we examine the application of revised scaled-particle theory (RSPT) to extrapolate molecular simulation results for the wetting of molecular-to-meso-scale repulsive solutes in liquid water and decane to determine the interfacial free energies of hard, flat surfaces. We show that the RSPT yields interfacial free energies at ambient pressures that are consistently greater than that obtained from the liquid-vapor surface tensions of water and decane by ∼4%. Nevertheless, the hard surface and liquid-vapor interfacial free energies are parallel over a broad temperature range at 1 bar indicating similar entropic contributions. With increasing pressure, the hard, flat interfacial free energies exhibit a maximum in the vicinity of ∼1000 bars. This non-monotonic behavior in both water and decane reflects solvent dewetting at low pressures, followed by wetting at higher pressures as the solvents are pushed onto the solute. By comparing the results of RSPT against classic scaled-particle theory (CSPT), we show that CSPT systematically predicts greater entropic penalties for interface formation and makes inconsistent predictions between the pressure dependence of the interfacial free energy and solvent contact density with the solute surface.

Interplay between Conformational Heterogeneity and Hydration in the Folding Landscape of a Designed Three-Helix Bundle

Water is known to play a critical role in protein folding and stability. Here we develop and employ a coarse-grained (CG) model to directly explore the role of water in shaping the conformational landscape explored during protein folding. For this purpose, we simulate a designed sequence with binary patterning of neutral and hydrophobic residues, which is capable of folding to a three-helix bundle in explicit water. We find two folded states of this sequence, with rotation of the helices occurring to trade between hydrophobic packing and water expulsion from the core. This work provides insight into the role of water and hydrophobicity in generating competing folded states for a protein.

Unified elucidation of the entropy-driven and -opposed hydrophobic effects

The association of nonpolar solutes is generally believed to be entropy driven, which has been shown to be true for the contact of small molecules, ellipsoids, and plates.

On the Role of Nonspherical Cavities in Short Length-Scale Density Fluctuations in Water

Density fluctuations in liquid water are at the heart of numerous phenomena associated with hydrophobic effects such as protein folding and the interaction between biomolecules. One of the most fundamental processes in this regard is the solvation of hydrophobic solutes in water. The vast majority of theoretical and numerical studies examine density fluctuations at the short length scale focusing exclusively on spherical cavities. In this work, we use both first-principles and classical molecular dynamics simulations to demonstrate that density fluctuations in liquid water can deviate significantly from the canonical spherical shapes. We show that regions of empty space are frequently characterized by exotic, highly asymmetric shapes that can be quite delocalized over the hydrogen bond network. Interestingly, density fluctuations of these shapes are characterized by Gaussian statistics with larger fluctuations. An important consequence of this is that the work required to create non spherical cavities can be substantially smaller than that of spheres. This feature is also qualitatively captured by the Lum-Chandler-Weeks theory. The scaling behavior of the free energy as a function of the volume at short length scales is qualitatively different for the nonspherical entities. We also demonstrate that nonspherical density fluctuations are important for accommodating the hydrophobic amino acid alanine and are thus likely to have significant implications when it comes to solvating highly asymmetrical species such as alkanes, polymers, or biomolecules.

Structure and dynamics of high- and low-density water molecules in the liquid and supercooled regimes

By combining the local structure index with potential energy minimisations we study the local environment of the water molecules for a couple of water models, TIP5P-Ew and SPC/E, in order to characterise low- and high-density "species". Both models show a similar behaviour within the supercooled regime, with two clearly distinguishable populations of unstructured and structured molecules, the fraction of the latter increasing with supercooling. Additionally, for TIP5P-Ew, we find that the structured component vanishes quickly at the normal liquid regime (above the melting temperature). Thus, while SPC/E provides a fraction of structured molecules similar to that found in X-ray experiments, we show that TIP5P-Ew underestimates such value. Moreover, unlike SPC/E, we demonstrate that TIP5P-Ew does not follow the linear dependence of the logarithm of the structured fraction with inverse temperature, as predicted by the two-order parameter model. Finally, we link structure to dynamics by showing that there exists a strong correlation between structural fluctuation and dynamics in the supercooled state with spatial correlations in both static and dynamic quantities.

The impact of surface area, volume, curvature, and Lennard-Jones potential to solvation modeling

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature-based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.

Ligand Shell Composition-Dependent Effects on the Apparent Hydrophobicity and Film Behavior of Gold Nanoparticles at the Air-Water Interface

Nanoparticles with well-defined interfacial energy and wetting properties are needed for a broad range of applications involving nanoparticle self-assembly including the formation of superlattices, stability of Pickering emulsions, and for the control of nanoparticle interactions with biological membranes. Theoretical, simulated, and recent experimental studies have found nanometer-scale chemical heterogeneity to have important effects on hydrophobic interactions. Here we report the study of 4 nm gold nanoparticles with compositionally well-defined mixed ligand shells of hydroxyl-(OH) and methyl-(CH3) terminated alkylthiols as Langmuir films. Compositions ranging from 0-25% hydroxyl were examined and reveal nonmonotonic changes in particle hydrophobicity at the air-water interface. Unlike nanoparticles capped exclusively with a methyl-terminated alkylthiol, extensive particle aggregation is found for ligand shells containing <2% hydroxyl-terminated chains. This aggregation was lessened upon increasing the quantity of OH-terminated chains. Nanoparticles capped with 25% OH yield films of well-separated nanoparticles exhibiting a fluid-phase regime in the surface pressure vs area isotherm. Compression-expansion hysteresis, monolayer collapse, and mean nanoparticle area measurements support the TEM-observed changes in film morphology. Such clear changes in the hydrophobicity of nanoparticles based on very small changes in the ligand shell composition are shown to impact the process of interfacial nanoparticle self-assembly and are an important demonstration of nanoscale wetting with consequences in both materials and biological applications of nanoparticles that require tunable hydrophobicity.

Recent developments in the theoretical, simulational, and experimental studies of the role of water hydrogen bonding in hydrophobic phenomena

Hydrophobic effects (hydrophobic hydration and hydrophobic interaction) constitute an important element of a wide variety of phenomena relevant to biological, physical, chemical, environmental, engineering, and pharmaceutical sciences, such as the immiscibility of oil and water, self-assembly of amphiphiles leading to micelle and membrane formation, folding and stability and unfolding of the native structure of a biologically active protein, gating of ion channels, wetting, froth floatation, and adhesion. On the other hand, the hydrogen bonding ability of water plays a major (if not crucial) role in hydrophobic phenomena. We present a review of most important and relatively recent experimental, simulational, and theoretical research on hydrophobic phenomena in various systems. With a particular interest we survey investigations clarifying the role of water hydrogen bonding therein, because it has been the main object of our own recent research. We have developed a probabilistic hydrogen bond (PHB) model that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of its distance to a hydrophobe, hydrophobe radius, and temperature. Knowing that function, one can explicitly identify a water hydrogen bond contribution to the external potential whereto a water molecule is subjected near a hydrophobe. Combining the PHB model with the classical density functional theory (DFT), one can examine the contribution of water hydrogen bonding to the temperature and lengthscale effects on the hydration of particles and on their solvent-mediated interactions over the entire low-to-high temperature and small-to-large lengthscale ranges. We applied the combined DFT/PHB model to study a variety of hydrophobic phenomena such as (liquid) water in contact with a hydrophobic plate, solvation of spherical solutes of various radii in associated and non-associated liquids at various temperatures, the solvent-mediated interaction of spherical solutes and its temperature dependence, interaction of C60 fullerenes in water, temperature effect on the evaporation lengthscale of water confined between two hydrophobes, temperature dependence of the effective width of the solute-solvent transition layer and average density therein. These applications demonstrated that the DFT/PHB model can serve as a valuable tool in studying hydrophobic phenomena because it constitutes a balanced combination of simplicity, accuracy, and detail. The predictions of the combined DFT/PHB approach for the solvent density profiles and thermodynamic aspects of hydrophobic phenomena are generally in good agreement with experiments and simulations. For example, it predicts the small-to-large crossover lengthscale of its mechanism to be approximately in the range from 1nm to 4nm, and decreasing with increasing temperature. It also suggests that, in terms of the average fluid density in the solute-solvent transition layer, the transition layer for small hydrophobes (of radii ≲2 nm) becomes enriched with rather than depleted of fluid when both the solvent-solute affinity and hb-energy alteration ratio become large enough. The boundary values of these parameters, needed for the depletion-to-enrichment crossover, are predicted to decrease with increasing temperature.