Static and dynamic correlations in water at hydrophobic interfaces

Computation of Overhauser dynamic nuclear polarization processes reveals fundamental correlation between water dynamics, structure, and solvent restructuring entropy

Hydration water dynamics, structure, and thermodynamics are crucially important to understand and predict water-mediated properties at molecular interfaces. Yet experimentally and directly quantifying water behavior locally near interfaces at the sub-nanometer scale is challenging, especially at interfaces submerged in biological solutions. Overhauser dynamic nuclear polarization (ODNP) experiments measure equilibrium hydration water dynamics within 8-15 angstroms of a nitroxide spin probe on instantaneous timescales (10 picoseconds to nanoseconds), making ODNP a powerful tool for probing local water dynamics in the vicinity of the spin probe. As with other spectroscopic techniques, concurrent computational analysis is necessary to gain access to detailed molecular level information about the dynamic, structural, and thermodynamic properties of water from experimental ODNP data. We chose a model system that can systematically tune the dynamics of water, a water-glycerol mixture with compositions ranging from 0 to 0.3 mole fraction glycerol. We demonstrate the ability of molecular dynamics (MD) simulations to compute ODNP spectroscopic quantities, and show that translational, rotational, and hydrogen bonding dynamics of hydration water align strongly with spectroscopic ODNP parameters. Moreover, MD simulations show tight correlations between the dynamic properties of water that ODNP captures and the structural and thermodynamic behavior of water. Hence, experimental ODNP readouts of varying water dynamics suggest changes in local structural and thermodynamic hydration water properties.

Relationships between Molecular Structural Order Parameters and Equilibrium Water Dynamics in Aqueous Mixtures

Water's unique thermophysical properties and how it mediates aqueous interactions between solutes have long been interpreted in terms of its collective molecular structure. The seminal work of Errington and Debenedetti [Nature 2001, 409, 318-321] revealed a striking hierarchy of relationships among the thermodynamic, dynamic, and structural properties of water, motivating many efforts to understand (1) what measures of water structure are connected to different experimentally accessible macroscopic responses and (2) how many such structural metrics are adequate to describe the collective structural behavior of water. Diffusivity constitutes a particularly interesting experimentally accessible equilibrium property to investigate such relationships because advanced NMR techniques allow the measurement of bulk and local water dynamics in nanometer proximity to molecules and interfaces, suggesting the enticing possibility of measuring local diffusivities that report on water structure. Here, we apply statistical learning methods to discover persistent structure-dynamic correlations across a variety of simulated aqueous mixtures, from alcohol-water to polypeptoid-water systems. We investigate a variety of molecular water structure metrics and find that an unsupervised statistical learning algorithm (namely, sequential feature selection) identifies only two or three independent structural metrics that are sufficient to predict water self-diffusivity accurately. Surprisingly, the translational diffusivity of water across all mixed systems studied here is strongly correlated with a measure of tetrahedral order given by water's triplet angle distribution. We also identify a separate small number of structural metrics that well predict an important thermodynamic property, the excess chemical potential of an idealized methane-sized hydrophobe in water. Ultimately, we offer a Bayesian method of inferring water structure by using only structure-dynamics linear regression models with experimental Overhauser dynamic nuclear polarization (ODNP) measurements of water self-diffusivity. This study thus quantifies the relationships among several distinct structural order parameters in water and, through statistical learning, reveals the potential to leverage molecular structure to predict fundamental thermophysical properties. In turn, these findings suggest a framework for solving the inverse problem of inferring water's molecular structure using experimental measurements such as ODNP studies that probe local water properties.

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.

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.

Connecting Non-Gaussian Water Density Fluctuations to the Lengthscale Dependent Crossover in Hydrophobic Hydration

We connect density fluctuations in liquid water to lengthscale dependent crossover in hydrophobic hydration. Specifically, we employ indirect umbrella sampling (INDUS) simulations to characterize density fluctuations in observation volumes of various sizes and shapes in water and as a function of temperature and salt concentration. Consistent with previous observations, density fluctuations are Gaussian in small molecular scale volumes, but they display non-Gaussian "low-density fat tails" in larger volumes. These non-Gaussian tails are indicative of the proximity of water to its liquid to vapor phase transition and have implications on biomolecular interactions and function. We show that the onset of non-Gaussian fluctuations in large volumes is accompanied by the formation of a cavity in the observation volume. We develop a model that uses the physics of cavity-water interface formation as a key ingredient and show that it captures the nature of non-Gaussian density fluctuations over a broad region in water and in salt solutions. We discuss the limitations of this model in the very low density region of the distribution. Our calculations provide new insights into the origins of non-Gaussian density fluctuations in water and their connections to lengthscale dependent crossover in hydrophobic hydration.

Hydration-mediated G-protein-coupled receptor activation

Although G-protein–coupled receptors (GPCRs) control vast physiological pathways, their activation remains chemically and physically enigmatic. Our osmotic stress studies of the visual receptor rhodopsin have redefined the standard model of GPCR signaling by revealing the essential role of bulk water. We show results consistent with a large number of water molecules flooding the rhodopsin interior during activation to stabilize the effector binding conformation. These results suggest a model of GPCR activation in which the receptor becomes solvent-swollen upon formation of the active state. We thus demonstrate the mechanism whereby water acts as a powerful allosteric modulator of a pharmacologically important membrane protein family.

The Rhodopsin family of G-protein–coupled receptors (GPCRs) comprises the targets of nearly a third of all pharmaceuticals. Despite structural water present in GPCR X-ray structures, the physiological relevance of these solvent molecules to rhodopsin signaling remains unknown. Here, we show experimental results consistent with the idea that rhodopsin activation in lipid membranes is coupled to bulk water movements into the protein. To quantify hydration changes, we measured reversible shifting of the metarhodopsin equilibrium due to osmotic stress using an extensive series of polyethylene glycol (PEG) osmolytes. We discovered clear evidence that light activation entails a large influx of bulk water (∼80–100 molecules) into the protein, giving insight into GPCR activation mechanisms. Various size polymer osmolytes directly control rhodopsin activation, in which large solutes are excluded from rhodopsin and dehydrate the protein, favoring the inactive state. In contrast, small osmolytes initially forward shift the activation equilibrium until a quantifiable saturation point is reached, similar to gain-of-function protein mutations. For the limit of increasing osmolyte size, a universal response of rhodopsin to osmotic stress is observed, suggesting it adopts a dynamic, hydrated sponge-like state upon photoactivation. Our results demand a rethinking of the role of water dynamics in modulating various intermediates in the GPCR energy landscape. We propose that besides bound water, an influx of bulk water plays a necessary role in establishing the active GPCR conformation that mediates signaling.

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.

Bridging Gaussian Density Fluctuations from Microscopic to Macroscopic Volumes: Applications to Non-Polar Solute Hydration Thermodynamics

The hydration of hydrophobic solutes is intimately related to the spontaneous formation of cavities in water through ambient density fluctuations. Information theory-based modeling and simulations have shown that water density fluctuations in small volumes are approximately Gaussian. For limiting cases of microscopic and macroscopic volumes, water density fluctuations are known exactly and are rigorously related to the density and isothermal compressibility of water. Here, we develop a theory—interpolated gaussian fluctuation theory (IGFT)—that builds an analytical bridge to describe water density fluctuations from microscopic to molecular scales. This theory requires no detailed information about the water structure beyond the effective size of a water molecule and quantities that are readily obtained from water’s equation-of-state—namely, the density and compressibility. Using simulations, we show that IGFT provides a good description of density fluctuations near the mean, that is, it characterizes the variance of occupancy fluctuations over all solute sizes. Moreover, when combined with the information theory, IGFT reproduces the well-known signatures of hydrophobic hydration, such as entropy convergence and solubility minima, for atomic-scale solutes smaller than the crossover length scale beyond which the Gaussian assumption breaks down. We further show that near hydrophobic and hydrophilic self-assembled monolayer surfaces in contact with water, the normalized solvent density fluctuations within observation volumes depend similarly on size as observed in the bulk, suggesting the feasibility of a modified version of IGFT for interfacial systems. Our work highlights the utility of a density fluctuation-based approach toward understanding and quantifying the solvation of non-polar solutes in water and the forces that drive them toward surfaces with different hydrophobicities.

Microenvironment-tailored nanoassemblies for the diagnosis and therapy of neurodegenerative diseases

Neurodegenerative disorder is an illness involving neural dysfunction/death attributed to complex pathological processes, which eventually lead to the mortality of the host. It is generally recognized through features such as mitochondrial dysfunction, protein aggregation, oxidative stress, metal ions dyshomeostasis, membrane potential change, neuroinflammation and neurotransmitter impairment. The aforementioned neuronal dysregulations result in the formation of a complex neurodegenerative microenvironment (NME), and may interact with each other, hindering the performance of therapeutics for neurodegenerative disease (ND). Recently, smart nanoassemblies prepared from functional nanoparticles, which possess the ability to interfere with different NME factors, have shown great promise to enhance the diagnostic and therapeutic efficacy of NDs. Herein, this review highlights the recent advances of stimuli-responsive nanoassemblies that can effectively combat the NME for the management of ND. The first section outlined the NME properties and their interrelations that are exploitable for nanoscale targeting. The discussion is then extended to the controlled assembly of functional nanoparticles for the construction of stimuli-responsive nanoassemblies. Further, the applications of stimuli-responsive nanoassemblies for the enhanced diagnosis and therapy of ND are introduced. Finally, perspectives on the future development of NME-tailored nanomedicines are given.

Simulation of FUS Protein Condensates with an Adapted Coarse-Grained Model

Disordered proteins and nucleic acids can condense into droplets that resemble the membraneless organelles observed in living cells. MD simulations offer a unique tool to characterize the molecular interactions governing the formation of these biomolecular condensates, their physicochemical properties, and the factors controlling their composition and size. However, biopolymer condensation depends sensitively on the balance between different energetic and entropic contributions. Here, we develop a general strategy to fine-tune the potential energy function for molecular dynamics simulations of biopolymer phase separation. We rebalance protein-protein interactions against solvation and entropic contributions to match the excess free energy of transferring proteins between dilute solution and condensate. We illustrate this formalism by simulating liquid droplet formation of the FUS low-complexity domain (LCD) with a rebalanced MARTINI model. By scaling the strength of the nonbonded interactions in the coarse-grained MARTINI potential energy function, we map out a phase diagram in the plane of protein concentration and interaction strength. Above a critical scaling factor of αc ≈ 0.6, FUS-LCD condensation is observed, where α = 1 and 0 correspond to full and repulsive interactions in the MARTINI model. For a scaling factor α = 0.65, we recover experimental densities of the dilute and dense phases, and thus the excess protein transfer free energy into the droplet and the saturation concentration where FUS-LCD condenses. In the region of phase separation, we simulate FUS-LCD droplets of four different sizes in stable equilibrium with the dilute phase and slabs of condensed FUS-LCD for tens of microseconds, and over one millisecond in aggregate. We determine surface tensions in the range of 0.01-0.4 mN/m from the fluctuations of the droplet shape and from the capillary-wave-like broadening of the interface between the two phases. From the dynamics of the protein end-to-end distance, we estimate shear viscosities from 0.001 to 0.02 Pa s for the FUS-LCD droplets with scaling factors α in the range of 0.625-0.75, where we observe liquid droplets. Significant hydration of the interior of the droplets keeps the proteins mobile and the droplets fluid.

From a bulk to nanoconfined water chain: bridge water at the pore of the (6,6) carbon nanotube

Hydrophobic porous materials with nano-pores are critical in many processes such as water desalination and biological membrane transportation. Herein, we performed molecular dynamics (MD) simulations on a prototypical hydrophobic nanochannel consisting of a (6,6) carbon nanotube (CNT) of 4.12 Å in radius and 13.72 Å in length immersed in water. The simulation shows that there are two major filling numbers of water N = 5 and N = 6, with the former being the most stable one. The confined waters form a single-file water chain with two hydrogen bonds per water. An extending water chain is formed for N = 5, with a bridge water near the pore of the CNT linking the water confined inside the CNT and hydration layer around the pore of the CNT. The bridge water can be considered as intermediate water characterized by three hydrogen bonds that distinguish from the confined water and bulk water. On the other hand, the hydration layer is depleted from the pore when N = 6. The analyses of the correlation of the bond order for the adjacent hydrogen bond pair of the hydration layer around the pore of the CNT does not show apparent difference from that of bulk water, though the former is slightly ordered. van Hove analysis of the bridge water shows that it tends to move inside the CNT when N < 5, in order to maintain the chemical equilibrium between the confined water and bulk water. This study highlights the unique structure of water around the hydrophobic pore of a sub-nanometer nanochannel.

First-passage fingerprints of water diffusion near glutamine surfaces

The extent to which biological interfaces affect the dynamics of water plays a key role in the exchange of matter and chemical interactions that are essential for life. The density and the mobility of water molecules depend on their proximity to biological interfaces and can play an important role in processes such as protein folding and aggregation. In this work, we study the dynamics of water near glutamine surfaces-a system of interest in studies of neurodegenerative diseases. Combining molecular-dynamics simulations and stochastic modelling, we study how the mean first-passage time and related statistics of water molecules escaping subnanometer-sized regions vary from the interface to the bulk. Our analysis reveals a dynamical complexity that reflects underlying chemical and geometrical properties of the glutamine surfaces. From the first-passage time statistics of water molecules, we infer their space-dependent diffusion coefficient in directions normal to the surfaces. Interestingly, our results suggest that the mobility of water varies over a longer length scale than the chemical potential associated with the water-protein interactions. The synergy of molecular dynamics and first-passage techniques opens the possibility for extracting space-dependent diffusion coefficients in more complex, inhomogeneous environments that are commonplace in living matter.

Water in Nanopores and Biological Channels: A Molecular Simulation Perspective

This Review explores the dynamic behavior of water within nanopores and biological channels in lipid bilayer membranes. We focus on molecular simulation studies, alongside selected structural and other experimental investigations. Structures of biological nanopores and channels are reviewed, emphasizing those high-resolution crystal structures, which reveal water molecules within the transmembrane pores, which can be used to aid the interpretation of simulation studies. Different levels of molecular simulations of water within nanopores are described, with a focus on molecular dynamics (MD). In particular, models of water for MD simulations are discussed in detail to provide an evaluation of their use in simulations of water in nanopores. Simulation studies of the behavior of water in idealized models of nanopores have revealed aspects of the organization and dynamics of nanoconfined water, including wetting/dewetting in narrow hydrophobic nanopores. A survey of simulation studies in a range of nonbiological nanopores is presented, including carbon nanotubes, synthetic nanopores, model peptide nanopores, track-etched nanopores in polymer membranes, and hydroxylated and functionalized nanoporous silica. These reveal a complex relationship between pore size/geometry, the nature of the pore lining, and rates of water transport. Wider nanopores with hydrophobic linings favor water flow whereas narrower hydrophobic pores may show dewetting. Simulation studies over the past decade of the behavior of water in a range of biological nanopores are described, including porins and β-barrel protein nanopores, aquaporins and related polar solute pores, and a number of different classes of ion channels. Water is shown to play a key role in proton transport in biological channels and in hydrophobic gating of ion channels. An overall picture emerges, whereby the behavior of water in a nanopore may be predicted as a function of its hydrophobicity and radius. This informs our understanding of the functions of diverse channel structures and will aid the design of novel nanopores. Thus, our current level of understanding allows for the design of a nanopore which promotes wetting over dewetting or vice versa. However, to design a novel nanopore, which enables fast, selective, and gated flow of water de novo would remain challenging, suggesting a need for further detailed simulations alongside experimental evaluation of more complex nanopore systems.

Molecular Mechanism of Gas Solubility in Liquid: Constant Chemical Potential Molecular Dynamics Simulations

Accurate prediction of gas solubility in a liquid is crucial in many areas of chemistry, and a detailed understanding of the molecular mechanism of the gas solvation continues to be an active area of research. Here, we extend the idea of the constant chemical potential molecular dynamics (CμMD) approach to the calculation of the gas solubility in the liquid under constant gas chemical potential conditions. As a representative example, we utilize this method to calculate the isothermal solubility of carbon dioxide in water. Additionally, we provide microscopic insight into the mechanism of solvation that preferentially occurs in areas of the surface where the hydrogen network is broken.

SJ, van der Vegt NFA. Characterizing Polymer Hydration Shell Compressibilities with the Small-System Method

The small-system method (SSM) exploits the unique feature of finite-sized open systems, whose thermodynamic quantities scale with the inverse system size. This scaling enables the calculation of properties in the thermodynamic limit of macroscopic systems based on computer simulations of finite-sized systems. We herein extend the SSM to characterize the hydration shell compressibility of a generic hydrophobic polymer in water. By systematically increasing the strength of polymer-water repulsion, we find that the excess inverse thermodynamic correction factor (Δ1/Γs∞) and compressibility (Δχs) of the first hydration shell change sign from negative to positive. This occurs with a concurrent decrease in water hydrogen bonding and local tetrahedral order of the hydration shell water. The crossover lengthscale corresponds to an effective polymer bead diameter of 0.7 nm and is consistent with previous works on hydration of small and large hydrophobic solutes. The crossover lengthscale in polymer hydration shell compressibility, herein identified with the SSM approach, relates to hydrophobic interactions and macromolecular conformational equilibria in aqueous solution. The SSM approach may further be applied to study thermodynamic properties of polymer solvation shells in mixed solvents.

Cavity Particle in Aqueous Solution with a Hydrophobic Solute: Structure, Energetics, and Functionals

Endpoints density functional theory (DFT) provides a framework for calculating the excess chemical potential of a solute in solution using solvent distribution functions obtained from both physical endpoints of a hypothetical charging process which transforms the solvent density from that of the pure liquid to the solution state. In this work, the endpoints DFT equations are formulated in terms of the indirect (solvent-mediated) contribution ω(x) to the solute-solvent potential of mean force, and their connections are established with the conventional DFT expressions which are based on the use of direct correlation functions. ω actually corresponds to the free-energy cost to move a cavity particle (a tagged solvent molecule which interacts with the other solvent molecules but not the solute) from the bulk to the configuration x of a solvent molecule relative to the solute and is a suitable variable to describe the solvent effects on the solute-solvent interactions. HNC and PY type approximations are then used to integrate the DFT charging integral involved in the exact expression for the excess chemical potential. With these approximations, molecular simulations are to be performed at the two endpoints of solute insertion: pure solvent without the solute and the solution system with the fully coupled solute-solvent interaction. An endpoints method thus utilizes the ensembles of intermolecular configurations of physical interest, which are often readily accessible with MD simulations given the present computational power. To illustrate properties of the formulation, we perform simulations of model systems consisting of a cavity particle in an aqueous solution containing a spherical hydrophobic solute of three different sizes from which ω(x) and the solute chemical potential can be calculated using endpoints DFT expressions. These are compared with corresponding results obtained using the approximations needed in order to evaluate the endpoints DFT charging integral when cavity particle simulation data is not available. We analyze a new approximation (two-points quadratic HNC) to the DFT charging integral which captures the correct behavior of the cavity distributions at both endpoints of the solute insertion. The behavior of the cavity particle in simple and complex liquids plays an important role in various theoretical treatments of the solute chemical potential. For pure Lennard-Jones fluids, the free energy to bring a cavity particle from the bulk to the center of a fluid particle is negative. However, for solutes of varying size, this is not generally true for Lennard-Jones fluids or the systems studied in this work. We carry out energetic and structural analyses of the cavity particle in aqueous solution with hydrophobic solutes of varying size and discuss the results in the context of the hydrophobic effect.

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.

Comparative Study of Anomalous Size Dependence of Charged and Neutral Solute Diffusion in Water

We present a comparative study of size dependence of diffusion for charged and neutral solutes in water. Although both show nonmonotonicity of the size dependence of diffusion, their nature and origin are quite different. For neutral solutes, the peak position and the value of diffusion at the maximum are both independent of the solute-water interaction. Interestingly, for charged solutes, with an increase in solute-water interaction strength, the peak position shifts to lower solute sizes and with an increase in charge, it shifts to higher solute sizes. The diffusion value at the peak reduces with an increase in both solute-water interaction and solute charge. We show that all these features observed for charged solutes can be understood in terms of the interplay between ionic and nonionic interactions which is definitely absent for neutral solutes. Some of the earlier studies addressing the nonmonotonicity in diffusion did suggest the interplay between the two interactions to be the cause. However, this is the first time we show that such an interplay gives rise to the nonmonotonicity in the potential energy which is a prerequisite for obtaining the nonmonotonicity in the diffusion. Such nonmonotonicity in the potential energy is absent for neutral solutes.

Effects of Packing Density and Chain Length on the Surface Hydrophobicity of Thin Films Composed of Perfluoroalkyl Acrylate Chains: A Molecular Dynamics Study

A good understanding of the surface hydrophobicity of fluorinated materials is useful for their application as coating materials. The present study investigates the surface hydrophobicity of perfluoroalkyl acrylate (PFA) thin films using molecular dynamics simulations. Surface hydrophobicity is characterized by examining the contact angle of a water droplet on PFA surfaces and the cavity formation free energy in the vicinity of the surface. It is found that the calculated microscopic contact angles are in good agreement with the experimental results and partially capture the difference in the hydrophobicity of the surface arising from the variation of packing density and side chain length of PFA. The variations of cavity formation free energy in the vicinity of the surface elucidate that the surface hydrophobicity is mainly governed by the packing density rather than the chain length of PFA. The hydrophobicity generally increases with decreasing the packing density to some extent and then turns to decrease as further reducing the packing density. At higher packing density, the surface hydrophobicity slightly decreases with increasing the chain length, while at the lower packing density, the surface hydrophobicity is increased when chain length of PFA is longer than six carbons. Furthermore, we found that the influence of packing density on the surface hydrophobicity is directly related to the variation of the surface roughness and chain flexibility, that is, the surface hydrophobicity increases with increase in the surface roughness, while the chain flexibility plays a secondary role in the enhancement by affecting the stability of water staying near the interface. The study provides a significant insight into the local hydrophobicity and microscopic structure of the PFA surfaces, which would be useful for the application of surface modification.

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.

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.

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.

Nanoscale dynamics of water confined in ordered mesoporous carbon

The single particle dynamics of water confined in ordered mesoporous carbon matrix was investigated in the temperature range from 290 K to 170 K by quasielastic neutron scattering using three high resolution neutron spectrometers.

High and low density patches in simulated liquid water

We present insights into the nature of structural heterogeneities in liquid water by characterizing the empty space within the hydrogen bond network. Using molecular dynamics simulations, we show that density fluctuations create regions of empty space characterized by a diverse morphology - from spherical to fractal-like voids. These voids allow for the identification of low and high density patches of the liquid, encompassing short (0.3-0.5 nm) as well as long (1-2 nm) length-scales. In addition, we show that the formation of these patches is coupled to collective fluctuations involving the topology of hydrogen-bonded rings of water molecules. In particular, water molecules in the high density patches tend to be slightly more tetrahedral - which is consistent with the predictions of the hydrophobic effect.

Single-file transport of water through membrane channels

Water at interfaces governs many processes on the molecular scale from electrochemical and enzymatic reactions to protein folding. Here we focus on water transport through proteinaceous pores that are so narrow that the water molecules cannot overtake each other in the pore. After a short introduction into the single-file transport theory, we analyze experiments in which the unitary water permeability, pf, of water channel proteins (aquaporins, AQPs), potassium channels (KcsA), and antibiotics (gramicidin-A derivatives) has been obtained. A short outline of the underlying methods (scanning electrochemical microscopy, fluorescence correlation spectroscopy, measurements of vesicle light scattering) is also provided. We conclude that pf increases exponentially with a decreasing number NH of hydrogen bond donating or accepting residues in the channel wall. The variance in NH is responsible for a more than hundredfold change in pf. The dehydration penalty at the channel mouth has a smaller effect on pf. The intricate link between pf and the Gibbs activation energy barrier, ΔG‡t, for water flow suggests that conformational transitions of water channels act as a third determinant of pf.

Modulation of Hydrophobic Interaction by Mediating Surface Nanoscale Structure and Chemistry, not Monotonically by Hydrophobicity

The hydrophobic (HB) interaction plays a critical role in many colloidal and interfacial phenomena, biophysical and industrial processes. Surface hydrophobicity, characterized by the water contact angle, is generally considered the most dominant parameter determining the HB interaction. Herein, we quantified the HB interactions between air bubbles and a series of hydrophobic surfaces with different nanoscale structures and surface chemistry in aqueous media using a bubble probe atomic force microscopy (AFM). Surprisingly, it is discovered that surfaces of similar hydrophobicity can show different ranges of HB interactions, while surfaces of different hydrophobicity can have similar ranges of HB interaction. The increased heterogeneity of the surface nanoscale structure and chemistry can effectively decrease the decay length of HB interaction from 1.60 nm to 0.35 nm. Our work provides insights into the physical mechanism of HB interaction.

Solvation in Space-time: Pretransition Effects in Trajectory Space

We demonstrate pretransition effects in space-time in trajectories of systems in which the dynamics displays a first-order phase transition between distinct dynamical phases. These effects are analogous to those observed for thermodynamic first-order phase transitions, most notably the hydrophobic effect in water. Considering the (infinite temperature) East model as an elementary example, we study the properties of "space-time solvation" by examining trajectories where finite space-time regions are conditioned to be inactive in an otherwise active phase. We find that solvating an inactive region of space-time within an active trajectory shows two regimes in the dynamical equivalent of solvation free energy: an "entropic" small solute regime in which uncorrelated fluctuations are sufficient to evacuate activity from the solute, and an "energetic" large solute regime which involves the formation of a solute-induced inactive domain with an associated active-inactive interface bearing a dynamical interfacial tension. We also show that as a result of this dynamical interfacial tension there is a dynamical analog of the hydrophobic collapse that drives the assembly of large hydrophobes in water. We discuss the general relevance of these results to the properties of dynamical fluctuations in systems with slow collective relaxation such as glass formers.

Role of Molecular Interactions and Protein Rearrangement in the Dissociation Kinetics of p38α MAP Kinase Type-I/II/III Inhibitors

Understanding the governing factors of fast or slow inhibitor binding/unbinding assists in developing drugs with preferred kinetic properties. For inhibitors with the same binding affinity targeting different binding sites of the same protein, the kinetic behavior can profoundly differ. In this study, we investigated unbinding kinetics and mechanisms of fast (type-I) and slow (type-II/III) binders of p38α mitogen-activated protein kinase, where the crystal structures showed that type-I and type-II/III inhibitors bind to pockets with different conformations of the Asp-Phe-Gly (DFG) motif. The work used methods that combine conventional molecular dynamics (MD), accelerated molecular dynamics (AMD) simulations, and the newly developed pathway search guided by internal motions (PSIM) method to find dissociation pathways. The study focuses on revealing key interactions and molecular rearrangements that hinder ligand dissociation by using umbrella sampling and post-MD processing to examine changes in free energy during ligand unbinding. As anticipated, the initial dissociation steps all require breaking interactions that appeared in crystal structures of the bound complexes. Interestingly, for type-I inhibitors such as SB2, p38α keeps barrier-free conformational fluctuation in the ligand-bound complex and during ligand dissociation. In contrast, with a type-II/III inhibitor such as BIRB796, with the rearrangements of p38α in its bound state, ligand unbinding features energetically unfavorable protein-ligand concerted movement. Our results also show that the type-II/III inhibitors preferred dissociation pathways through the allosteric channel, which is consistent with an existing publication. The study suggests that the level of required protein rearrangement is one major determining factor of drug binding kinetics in p38α systems, providing useful information for development of inhibitors.

Termination of Biological Function at Low Temperatures: Glass or Structural Transition?

Energy of life is produced by electron transfer in energy chains of respiration or photosynthesis. A small input of free energy available to biology puts significant restrictions on how much free energy can be lost in each electron-transfer reaction. We advocate the view that breaking ergodicity, leading to violation of the fluctuation-dissipation theorem (FDT), is how proteins achieve high reaction rates without sacrificing the reaction free energy. Here we show that a significant level of nonergodicity, represented by a large extent of the configurational temperature over the kinetic temperature, is maintained in the entire physiological range for the cytochrome c electron transfer protein. The protein returns to the state consistent with the FDT below the crossover temperature close to the temperature of the protein glass transition. This crossover leads to a sharp increase in the activation barrier of electron transfer and is displayed by a kink in the Arrhenius plot for the reaction rate constant.

Extent of Surface Force Additivity on Chemically Heterogeneous Substrates at Varied Orientations

Surface interactions between chemically mixed surfaces, as well as those among dissolved biomolecules, comprise distinct contributions from polar and hydrophobic moieties. These contributions are often context dependent. Approximate compliance to the Cassie additivity equation for the wetting free energies on mixed surfaces in water is, however, indicative of similarly additive forces between individual surface elements, suggesting a quadratic interpolation model for total force from the forces between pure surfaces. We use molecular dynamics/umbrella sampling simulations of parallel and nonparallel mixed surfaces with demonstrable Cassie-like behavior to verify how well the total surface force between the heterogeneous, molecularly rough surfaces can be approximated as a combination of forces among the homogeneous ones. When accounting for dissimilar distances of approach between functional groups of different types, our results for graphene surfaces with mixed methyl and nitrile coating show such a superposition to provide a reasonable first order approximation of interactions between the platelets. Deviations from additivity are more prominent in parallel-plate configurations, at high content of hydrophobic groups, and small separations. The inclusion of water polarizability does not visibly alter the observed behavior regardless of platelet orientations. The outcome of this study determines the necessary molecular conditions for observing force additivity that emphasize the context dependence of hydrophobic interaction in the presence of polar groups. This notion provides guidelines for the syntheses of new, chemically heterogeneous materials with tailored function-oriented properties in aqueous media.

Molecular Shape and the Hydrophobic Effect

This review focuses on papers published since 2000 on the topic of the properties of solutes in water. More specifically, it evaluates the state of the art of our understanding of the complex relationship between the shape of a hydrophobe and the hydrophobic effect. To highlight this, we present a selection of references covering both empirical and molecular dynamics studies of small (molecular-scale) solutes. These include empirical studies of small molecules, synthetic hosts, crystalline monolayers, and proteins, as well as in silico investigations of entities such as idealized hard and soft spheres, small solutes, hydrophobic plates, artificial concavity, molecular hosts, carbon nanotubes and spheres, and proteins.

Hydrophobicity of proteins and nanostructured solutes is governed by topographical and chemical context

Hydrophobic interactions drive many important biomolecular self-assembly phenomena. However, characterizing hydrophobicity at the nanoscale has remained a challenge due to its nontrivial dependence on the chemistry and topography of biomolecular surfaces. Here we use molecular simulations coupled with enhanced sampling methods to systematically displace water molecules from the hydration shells of nanostructured solutes and calculate the free energetics of interfacial water density fluctuations, which quantify the extent of solute-water adhesion, and therefore solute hydrophobicity. In particular, we characterize the hydrophobicity of curved graphene sheets, self-assembled monolayers (SAMs) with chemical patterns, and mutants of the protein hydrophobin-II. We find that water density fluctuations are enhanced near concave nonpolar surfaces compared with those near flat or convex ones, suggesting that concave surfaces are more hydrophobic. We also find that patterned SAMs and protein mutants, having the same number of nonpolar and polar sites but different geometrical arrangements, can display significantly different strengths of adhesion with water. Specifically, hydroxyl groups reduce the hydrophobicity of methyl-terminated SAMs most effectively not when they are clustered together but when they are separated by one methyl group. Hydrophobin-II mutants show that a charged amino acid reduces the hydrophobicity of a large nonpolar patch when placed at its center, rather than at its edge. Our results highlight the power of water density fluctuations-based measures to characterize the hydrophobicity of nanoscale surfaces and caution against the use of additive approximations, such as the commonly used surface area models or hydropathy scales for characterizing biomolecular hydrophobicity and the associated driving forces of assembly.

Excess Volumes from the Pressure Derivative of the Excess Chemical Potential: Testing Simple Models for Cavity Formation in Water

Excess volumes and excess compressibilities for hard spheres in water were computed by pressure derivatives of the excess chemical potential, which is equivalent to the work of cavity formation. This is relevant to the application of continuum solvation methods at various pressures. The excess chemical potential was modeled within phenomenological expressions for curved surfaces plus a pressure-volume term, for which two approaches were adopted, differing for the radius of the spherical volume. This implies a different dependence on pressure of parameters. In all cases, in the surface term, for the pressure derivative of parameters of the curvature function, use was made of the previously proposed expressions for the first two moments obtained from the density and radial distribution of oxygens in liquid water. Only for the parameter which has the dimension of surface tension (γ̃) was explicit dependence on pressure considered and results are affected by the specific polynomial used. In agreement with what inferred from simulation results obtained for cavities in TIP4P water, negative and positive adsorptions at the contact radius were extrapolated for a very large cavity at 1 and 8000 atm, respectively. The expressions here employed for the excess chemical potential predict the zero value of asymptotic adsorption to be at a pressure between 500 and 800 atm, which can be compared to results from the revised scaled particle theory. In the same range, for a nanometer-sized cavity, a change of behavior occurs regarding the ratio between the excess Helmholtz free energy and the product between pressure and excess volume.

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.

Spontaneous recovery of superhydrophobicity on nanotextured surfaces

Rough or textured hydrophobic surfaces are dubbed "superhydrophobic" due to their numerous desirable properties, such as water repellency and interfacial slip. Superhydrophobicity stems from an aversion of water for the hydrophobic surface texture, so that a water droplet in the superhydrophobic "Cassie state" contacts only the tips of the rough surface. However, superhydrophobicity is remarkably fragile and can break down due to the wetting of the surface texture to yield the "Wenzel state" under various conditions, such as elevated pressures or droplet impact. Moreover, due to large energetic barriers that impede the reverse transition (dewetting), this breakdown in superhydrophobicity is widely believed to be irreversible. Using molecular simulations in conjunction with enhanced sampling techniques, here we show that on surfaces with nanoscale texture, water density fluctuations can lead to a reduction in the free energetic barriers to dewetting by circumventing the classical dewetting pathways. In particular, the fluctuation-mediated dewetting pathway involves a number of transitions between distinct dewetted morphologies, with each transition lowering the resistance to dewetting. Importantly, an understanding of the mechanistic pathways to dewetting and their dependence on pressure allows us to augment the surface texture design, so that the barriers to dewetting are eliminated altogether and the Wenzel state becomes unstable at ambient conditions. Such robust surfaces, which defy classical expectations and can spontaneously recover their superhydrophobicity, could have widespread importance, from underwater operation to phase-change heat transfer applications.

Necessity of capillary modes in a minimal model of nanoscale hydrophobic solvation

Modern theories of the hydrophobic effect highlight its dependence on length scale, emphasizing the importance of interfaces in the vicinity of sizable hydrophobes. We recently showed that a faithful treatment of such nanoscale interfaces requires careful attention to the statistics of capillary waves, with significant quantitative implications for the calculation of solvation thermodynamics. Here, we show that a coarse-grained lattice model like that of Chandler [Chandler D (2005)Nature437(7059):640-647], when informed by this understanding, can capture a broad range of hydrophobic behaviors with striking accuracy. Specifically, we calculate probability distributions for microscopic density fluctuations that agree very well with results of atomistic simulations, even many SDs from the mean and even for probe volumes in highly heterogeneous environments. This accuracy is achieved without adjustment of free parameters, because the model is fully specified by well-known properties of liquid water. As examples of its utility, we compute the free-energy profile for a solute crossing the air-water interface, as well as the thermodynamic cost of evacuating the space between extended nanoscale surfaces. These calculations suggest that a highly reduced model for aqueous solvation can enable efficient multiscale modeling of spatial organization driven by hydrophobic and interfacial forces.

Pre-transition effects mediate forces of assembly between transmembrane proteins

We present a mechanism for a generic, powerful force of assembly and mobility for transmembrane proteins in lipid bilayers. This force is a pre-transition (or pre-melting) effect for the first-order transition between ordered and disordered phases in the membrane. Using large-scale molecular simulation, we show that a protein with hydrophobic thickness equal to that of the disordered phase embedded in an ordered bilayer stabilizes a microscopic order–disorder interface. The stiffness of that interface is finite. When two such proteins approach each other, they assemble because assembly reduces the net interfacial energy. Analogous to the hydrophobic effect, we refer to this phenomenon as the 'orderphobic effect'. The effect is mediated by proximity to the order–disorder phase transition and the size and hydrophobic mismatch of the protein. The strength and range of forces arising from this effect are significantly larger than those that could arise from membrane elasticity for the membranes considered.

DOI:http://dx.doi.org/10.7554/eLife.13150.001

The membrane that surrounds cells provides a selective barrier that allows some molecules through, but blocks the path of others. A cell’s membrane is made up of two layers of molecules with oily tails, and is therefore known as a bilayer. Many proteins are dotted within and on the inner and outer surfaces of the bilayer: some act as channels that control what goes in and out of the cell, while others protrude outside the cell so that they can sense changes in the environment.

Membrane proteins can move and interact within the bilayer, and various models have emerged to try to explain this dynamic system. These models are based on the membrane having some fluidity but also having regions where there is more structure, and typically describe the proteins as ordered clusters floating in an otherwise disordered fluid membrane. However, many researchers now think some proteins that pass through both layers of the bilayer (i.e., transmembrane proteins) make membranes more ordered, with a possibly gel-like state. However, it is not clear how transmembrane proteins can move and assemble together within such a relatively rigid membrane.

To investigate this, Katira, Mandadapu, Vaikuntanathan et al. carried out computer simulations using a model of a simple bilayer membrane. This membrane can exist in an ordered state, where the oily tails are neatly aligned, or a disordered state, where they are irregularly packed. Virtual ‘heating’ of the membrane caused it to shift from an ordered to a disordered state. When a simple transmembrane protein favoring the disordered state was inserted into the ordered state of the modeled membrane, disordered regions formed locally around the protein and the protein was able to diffuse within the membrane.

Modeling what would happen if two transmembrane proteins approached each other revealed that a consequence of the order–disorder transition is a strong attractive force that assembles the proteins together. Katira, Mandadapu, Vaikuntanathan et al. named this new phenomenon the 'orderphobic effect'. The forces arising from this effect were much greater than those currently believed to contribute to the assembly of membrane protein complexes, such as those generated by the elasticity of the membrane. This means that the orderphobic effect may be responsible for generating the protein clusters commonly seen in cell membranes.

Future work should next explore the opposite effect, where proteins favoring the ordered state are inserted into the disordered state of a membrane. This is expected to cause clustering of such proteins and thus large ordered regions in an otherwise disordered membrane.

DOI:http://dx.doi.org/10.7554/eLife.13150.002

Non-covalent interaction of benzene with methanol and diethyl ether solid surfaces

We have investigated the interactions involved at the interface of binary, layered ices (benzene on methanol and on diethyl ether) by means of laboratory experiments and ab initio calculations on model clusters.