Quantifying water density fluctuations and compressibility of hydration shells of hydrophobic solutes and proteins

What is the best simulation approach for measuring local density fluctuations near solvo-/hydrophobes?

Measurements of local density fluctuations are crucial to characterizing the interfacial properties of equilibrium fluids. A specific case that has been well-explored involves the heightened compressibility of water near hydrophobic entities. Commonly, a spatial profile of local fluctuation strength is constructed from the measurements of the mean and variance of solvent particle number fluctuations in a set of contiguous subvolumes of the system adjacent to the solvo-/hydrophobe. An alternative measure proposed by Evans and Stewart [J. Phys.: Condens. Matter 27, 194111 (2015)] defines a local compressibility profile in terms of the chemical potential derivative of the spatial number density profile. Using Grand canonical Monte Carlo simulation, we compare and contrast the efficacy of these two approaches for a Lennard-Jones solvent at spherical and planar solvophobic interfaces and SPC/E water at a hydrophobic spherical solute. Our principal findings are as follows: (i) the local compressibility profile χ(r) of Evans and Stewart is considerably more sensitive to variations in the strength of local density fluctuations than the spatial fluctuation profile F(r) and can resolve much more detailed structure; and (ii) while the local compressibility profile is essentially independent of the choice of spatial discretization used to construct the profile, the spatial fluctuation profile exhibits a strong systematic dependence on the size of the subvolumes on which the profile is defined. We clarify the origin and nature of this finite-size effect.

An Affordable Topography-Based Protocol for Assigning a Residue's Character on a Hydropathy (PARCH) Scale

The hydropathy of proteins or quantitative assessment of protein-water interactions has been a topic of interest for decades. Most hydropathy scales use a residue-based or atom-based approach to assign fixed numerical values to the 20 amino acids and categorize them as hydrophilic, hydroneutral, or hydrophobic. These scales overlook the protein's nanoscale topography, such as bumps, crevices, cavities, clefts, pockets, and channels, in calculating the hydropathy of the residues. Some recent studies have included protein topography in determining hydrophobic patches on protein surfaces, but these methods do not provide a hydropathy scale. To overcome the limitations in the existing methods, we have developed a Protocol for Assigning a Residue's Character on the Hydropathy (PARCH) scale that adopts a holistic approach to assigning the hydropathy of a residue. The parch scale evaluates the collective response of the water molecules in the protein's first hydration shell to increasing temperatures. We performed the parch analysis of a set of well-studied proteins that include the following─enzymes, immune proteins, and integral membrane proteins, as well as fungal and virus capsid proteins. Since the parch scale evaluates every residue based on its location, a residue may have very different parch values inside a crevice versus a surface bump. Thus, a residue can have a range of parch values (or hydropathies) dictated by the local geometry. The parch scale calculations are computationally inexpensive and can compare hydropathies of different proteins. The parch analysis can affordably and reliably aid in designing nanostructured surfaces, identifying hydrophilic and hydrophobic patches, and drug discovery.

Thermoresponsive Polymers under Pressure with a Focus on Poly(N-isopropylacrylamide) (PNIPAM)

Pressure is a key variable in the phase behavior of responsive polymers, both for applications and from a fundamental point of view. In this feature article, we review recent developments, particularly applications of neutron techniques such as small-angle neutron scattering (SANS) and quasi-elastic neutron scattering (QENS), across the temperature-pressure phase diagram. These are complemented by kinetic SANS experiments following pressure jumps. In the prototype system poly(N-isopropylacrylamide) (PNIPAM), QENS revealed the pressure-dependent characteristics of hydration water around the lower critical solution temperature transition. The size, water content, and inner structure of the mesoglobules formed in the two-phase region depend strongly on pressure, as shown by SANS. Beside these changes at the phase transition, the mesoglobule formation at low pressure is determined by kinetic factors, namely the formation of a polymer-rich, rigid shell, which hampers further growth by coalescence. At high pressure, in contrast, the growth proceeds by diffusion-limited coalescence without any kinetic hindrance. The disintegration of the mesoglobules evolves either via chain release from their surface or via swelling, depending on the osmotic pressure of the water. Moreover, we report on the profound influence of pressure on the cononsolvency effect. In the temperature-pressure frame, the one-phase region is hugely expanded upon the addition of the cosolvent methanol. SANS experiments unveil the enthalpic and entropic contributions to the effective Flory-Huggins interaction parameter between the segments and the solvent mixture. QENS experiments demonstrate an increase in polymer associated water with pressure, whereas methanol is released. Correspondingly, the solvent phase becomes enriched in methanol, providing a mechanism for the breakdown of cononsolvency at a high pressure. Finally, we outline future opportunities for high-pressure studies of thermoresponsive polymers, with a focus on neutron methods.

Comparative Analysis of Protein Surface Hydrophobicity Maps Determined by Sparse Sampling INDUS and Spatial Aggregation Propensity

Protein surface hydrophobicity plays a central role in various biological processes such as protein folding and aggregation, as well as in the design and manufacturing of biotherapeutics. While the hydrophobicity of protein surface patches has been linked to their constituent residue hydropathies, recent research has shown that protein surface hydrophobicity is more complex and characterized by the response of water to these surfaces. In this work, we employ water density perturbations to map the surface hydrophobicity of a set of model proteins using sparse indirect umbrella sampling simulations (SSI). This technique is used to identify hydrophobic surface patches for the set of model proteins, and the results are compared to those obtained from the widely adopted spatial aggregation propensity (SAP) technique. While SAP-based calculations show agreement with SSI in some cases, there are several examples of disagreement. We identify four general classes of difference in behavior and study factors that contribute to these differences. We find that the SAP method can sometimes mask the effect of weakly nonpolar or isolated nonpolar residues that can lead to strong hydrophobic patches on the protein surface. In addition, hydrophobic patches identified by SAP can exhibit shifts in both position and strength on the SSI map. Our results demonstrate that the combination of topography and chemical context controls the hydrophobicity of a given patch above and beyond the intrinsic polarity of the residues present on the patch surface. The availability of more accurate protein hydrophobicity maps in concert with new classes of hydrophobic molecular descriptors may create significant opportunities for in silico prediction of protein behavior for a range of applications, such as protein design, biomanufacturability, and downstream bioprocessing.

Extraction of Polyphenols from Slovenian Hop (Humulus lupulus L.) Aurora Variety Using Deep Eutectic Solvents: Choice of the Extraction Method vs. Structure of the Solvent

Polyphenols from Slovenian hops (Humulus lupulus L.) of the Aurora variety were extracted by different methods and using classical solvents and several deep eutectic solvents (DES) based on choline chloride as the hydrogen bond acceptor component. The obtained extract solutions were analyzed by HPLC for the content of extracted α- and β-acids and extracted xanthohumol. It was found that choline chloride:phenol DES concentrated aqueous solution had an extraction efficiency close to that of diethyl ether, which is considered one of the best classical extraction solvents for polyphenols from hops. The comparison of the extraction efficiency with other choline chloride-based DESs showed that the chemical similarity of the phenol ring in the solvent DES with the polyphenols in hops may be crucial for a highly efficient extraction with choline chloride:phenol DES. On the other hand, the choice of extraction method and the viscosity of the solvents tested seem to play only a minor role in this respect. As far as we know, this is the first study to attempt to relate extraction efficiency in the extraction of hydrophobic solutes to the compressibility of the DES extractants, the latter of which may be correlated with the extent of hydrophobic hydration around the DES components. In addition, using the heating and stirring method for the preparation of choline chloride-based DES concentrated aqueous solutions we found no support for the occurrence of water in two different roles (in the structural and in the dilution role) in these solvents.

Molecular Dynamics Investigation of Nanoscale Hydrophobicity of Polymer Surfaces: What Makes Water Wet?

The wettability of a polymer surface─related to its hydrophobicity or tendency to repel water─can be crucial for determining its utility, such as for a coating or a purification membrane. While wettability is commonly associated with the macroscopic measurement of a contact angle between surface, water, and air, the molecular physics that underlie these macroscopic observations are not fully known, and anticipating the relative behavior of different polymers is challenging. To address this gap in molecular-level understanding, we use molecular dynamics simulations to investigate and contrast interactions of water with six chemically distinct polymers: polytetrafluoroethylene, polyethylene, polyvinyl chloride, poly(methyl methacrylate), Nylon-66, and poly(vinyl alcohol). We show that several prospective quantitative metrics for hydrophobicity agree well with experimental contact angles. Moreover, the behavior of water in proximity to these polymer surfaces can be distinguished with analysis of interfacial water dynamics, extent of hydrogen bonding, and molecular orientation─even when macroscopic measures of hydrophobicity are similar. The predominant factor dictating wettability is found to be the extent of hydrogen bonding between polymer and water, but the precise manifestation of hydrogen bonding and its impact on surface water structure varies. In the absence of hydrogen bonding, other molecular interactions and polymer mechanics control hydrophobic ordering. These results provide new insights into how polymer chemistry specifically impacts water-polymer interactions and translates to surface hydrophobicity. Such factors may facilitate the design or processing of polymer surfaces to achieve targeted wetting behavior, and presented analyses can be useful in studying the interfacial physics of other systems.

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.

Solvation shell thermodynamics of extended hydrophobic solutes in mixed solvents

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

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.

Direct Calculation of Entropic Components in Cohesive Interaction Free Energies

Cohesive interaction free energies entail an entropic component related to fluctuations of the energy associated with the attractive portion of the solute-solvent potential. The corresponding "fluctuation entropy" is fundamental in the solvation thermodynamics of macromolecular solutes and is linked to interfacial solvent density fluctuations and hydrophobic effects. Since the direct calculation of fluctuation entropy in molecular simulations is hampered by the poor sampling of high-energy tails in the solute-solvent energy distribution, indirect, and often approximate, routes for the calculation of fluctuation entropy are usually required, involving the modeling of geometrically frozen repulsive solute cavities in thermodynamic integration approaches. Herein, we propose a method to directly compute the fluctuation entropy by employing indirect umbrella sampling (INDUS). To validate the method, we consider model systems consisting of subnanometer oil droplets in water for which the fluctuation entropy can be computed exactly using indirect methods. The fluctuation entropy calculated with the newly proposed direct method agrees with the indirect reference calculations. We also observe that the solvation free energy and the contribution of the fluctuation entropy to it are of comparable magnitudes, particularly for larger oil droplets (∼1 nm). The proposed method can readily be employed for flexible macromolecular solutes and systems with extended hydrophobic surfaces or in the vicinity of a dewetting transition.

Local Mutations Can Serve as a Game Changer for Global Protein Solvent Interaction

Although it is well-known that limited local mutations of enzymes, such as matrix metalloproteinases (MMPs), may change enzyme activity by orders of magnitude as well as its stability, the completely rational design of proteins is still challenging. These local changes alter the electrostatic potential and thus local electrostatic fields, which impacts the dynamics of water molecules close the protein surface. Here we show by a combined computational design, experimental, and molecular dynamics (MD) study that local mutations have not only a local but also a global effect on the solvent: In the specific case of the matrix metalloprotease MMP14, we found that the nature of local mutations, coupled with surface morphology, have the ability to influence large patches of the water hydrogen-bonding network at the protein surface, which is correlated with stability. The solvent contribution can be experimentally probed via terahertz (THz) spectroscopy, thus opening the door to the exciting perspective of rational protein design in which a systematic tuning of hydration water properties allows manipulation of protein stability and enzymatic activity.

Length-Scale Effects in Hydrophobic Polymer Collapse Transitions

The study of molecular mechanisms for cosolvent-driven hydrophobic polymer collapse transitions in water is of pivotal importance in the field of smart responsive materials. Computational studies together with complementary experimental data have led to the discovery and understanding of new phenomena in recent years. However, elementary mechanisms, generally contributing to polymer coil-globule transitions in different classes of cosolvent-water systems, remain elusive due to compensating energy-entropy effects. Herein, I discuss the role of length scales in polymer solubility problems. New ideas on surfactant mechanisms are discussed based on examples in which these mechanisms drive polymer swelling or collapse.

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

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

The key role of solvent in condensation: Mapping water in liquid-liquid phase-separated FUS

Formation of biomolecular condensates through liquid-liquid phase separation (LLPS) has emerged as a pervasive principle in cell biology, allowing compartmentalization and spatiotemporal regulation of dynamic cellular processes. Proteins that form condensates under physiological conditions often contain intrinsically disordered regions with low-complexity domains. Among them, the RNA-binding proteins FUS and TDP-43 have been a focus of intense investigation because aberrant condensation and aggregation of these proteins is linked to neurodegenerative diseases such as amyotrophic lateral sclerosis and frontotemporal dementia. LLPS occurs when protein-rich condensates form surrounded by a dilute aqueous solution. LLPS is per se entropically unfavorable. Energetically favorable multivalent protein-protein interactions are one important aspect to offset entropic costs. Another proposed aspect is the release of entropically unfavorable preordered hydration water into the bulk. We used attenuated total reflection spectroscopy in the terahertz frequency range to characterize the changes in the hydrogen bonding network accompanying the FUS enrichment in liquid-liquid phase-separated droplets to provide experimental evidence for the key role of the solvent as a thermodynamic driving force. The FUS concentration inside LLPS droplets was determined to be increased to 2.0 mM independent of the initial protein concentration (5 or 10 μM solutions) by fluorescence measurements. With terahertz spectroscopy, we revealed a dewetting of hydrophobic side chains in phase-separated FUS. Thus, the release of entropically unfavorable water populations into the bulk goes hand in hand with enthalpically favorable protein-protein interaction. Both changes are energetically favorable, and our study shows that both contribute to the thermodynamic driving force in phase separation.

The Interplay of Ligand Properties and Core Size Dictates the Hydrophobicity of Monolayer-Protected Gold Nanoparticles

The hydrophobicity of monolayer-protected gold nanoparticles is a crucial design parameter that influences self-assembly, preferential binding to proteins and membranes, and other nano-bio interactions. Predicting the effects of monolayer components on nanoparticle hydrophobicity is challenging due to the nonadditive, cooperative perturbations to interfacial water structure that dictate hydrophobicity at the nanoscale. In this work, we quantify nanoparticle hydrophobicity by using atomistic molecular dynamics simulations to calculate local hydration free energies at the nanoparticle-water interface. The simulations reveal that the hydrophobicity of large gold nanoparticles is determined primarily by ligand end group chemistry, as expected. However, for small gold nanoparticles, long alkanethiol ligands interact to form anisotropic bundles that lead to substantial spatial variations in hydrophobicity even for homogeneous monolayer compositions. We further show that nanoparticle hydrophobicity is modulated by changing the ligand structure, ligand chemistry, and gold core size, emphasizing that single-ligand properties alone are insufficient to characterize hydrophobicity. Finally, we illustrate that hydration free energy measurements correlate with the preferential binding of propane as a representative hydrophobic probe molecule. Together, these results show that both physical and chemical properties influence the hydrophobicity of small nanoparticles and must be considered together when predicting gold nanoparticle interactions with biomolecules.

Protein flexibility reduces solvent-mediated friction barriers of ligand binding to a hydrophobic surface patch

Solvent fluctuations have been explored in detail for idealized and rigid hydrophobic model systems, but so far it has remained unclear how internal protein motions and their coupling to the surrounding solvent affect the dynamics of ligand binding to biomolecular surfaces. Here, molecular dynamics simulations were used to elucidate the solvent-mediated binding of a model ligand to the hydrophobic surface patch of ubiquitin. The ligand's friction profiles reveal pronounced long-time correlations and enhanced friction in the vicinity of the protein, similar to idealized hydrophobic surfaces. Interestingly, these effects are shaped by internal protein motions. Protein flexibility modulates water density fluctuations near the hydrophobic surface patch and smooths out the friction profile of ligand binding.

Affinity of small-molecule solutes to hydrophobic, hydrophilic, and chemically patterned interfaces in aqueous solution

Performance of membranes for water purification is highly influenced by the interactions of solvated species with membrane surfaces, including surface adsorption of solutes upon fouling. Current efforts toward fouling-resistant membranes often pursue surface hydrophilization, frequently motivated by macroscopic measures of hydrophilicity, because hydrophobicity is thought to increase solute-surface affinity. While this heuristic has driven diverse membrane functionalization strategies, here we build on advances in the theory of hydrophobicity to critically examine the relevance of macroscopic characterizations of solute-surface affinity. Specifically, we use molecular simulations to quantify the affinities to model hydroxyl- and methyl-functionalized surfaces of small, chemically diverse, charge-neutral solutes represented in produced water. We show that surface affinities correlate poorly with two conventional measures of solute hydrophobicity, gas-phase water solubility and oil-water partitioning. Moreover, we find that all solutes show attraction to the hydrophobic surface and most to the hydrophilic one, in contrast to macroscopically based hydrophobicity heuristics. We explain these results by decomposing affinities into direct solute interaction energies (which dominate on hydroxyl surfaces) and water restructuring penalties (which dominate on methyl surfaces). Finally, we use an inverse design algorithm to show how heterogeneous surfaces, with multiple functional groups, can be patterned to manipulate solute affinity and selectivity. These findings, importantly based on a range of solute and surface chemistries, illustrate that conventional macroscopic hydrophobicity metrics can fail to predict solute-surface affinity, and that molecular-scale surface chemical patterning significantly influences affinity-suggesting design opportunities for water purification membranes and other engineered interfaces involving aqueous solute-surface interactions.

Protein Unfolding and Aggregation near a Hydrophobic Interface

The behavior of proteins near interfaces is relevant for biological and medical purposes. Previous results in bulk show that, when the protein concentration increases, the proteins unfold and, at higher concentrations, aggregate. Here, we study how the presence of a hydrophobic surface affects this course of events. To this goal, we use a coarse-grained model of proteins and study by simulations their folding and aggregation near an ideal hydrophobic surface in an aqueous environment by changing parameters such as temperature and hydrophobic strength, related, e.g., to ions concentration. We show that the hydrophobic surface, as well as the other parameters, affect both the protein unfolding and aggregation. We discuss the interpretation of these results and define future lines for further analysis, with their possible implications in neurodegenerative diseases.

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.

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.

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.

Screening of Coulomb interactions in liquid dielectrics

The interaction of charges in dielectric materials is screened by the dielectric constant of the bulk dielectric. In dielectric theories, screening is assigned to surface charges appearing from preferential orientations of dipoles along the local field in the interface. For liquid dielectrics, such interfacial orientations are affected by the interfacial structure characterized by a separate interfacial dipolar susceptibility. We argue that dielectric properties of polar liquids should be characterized by two distinct susceptibilities responsible for local response (solvation) and long-range response (dielectric screening). A microscopic model for dipolar screening in polar liquids is developed here. It shows that the standard bulk dielectric constant is responsible for screening at large distances. The potential of mean force between ions in polar liquids becomes oscillatory at short distances. Oscillations arise from the coupling of collective longitudinal excitations (dipolarons) of the polar liquid with its interfacial density profile. Interfacial electrostatics demonstrates a crossover beyond the solute radius of  ∼1 nm from the scaling laws roughly consistent with continuum expectations for small solutes to new scaling trends characterizing the much softer nano-scale solute-solvent interface. This crossover also marks the transition to a continuum-type electrostatic screening between ions, when short-distance oscillation of the potential of mean force become strongly damped. Screening oscillations are enhanced for more structured interfaces.

Hydrophobic Surface Enhances Electrostatic Interaction in Water

A high dielectric constant is one of the peculiar properties of liquid water, indicating that the electrostatic interaction between charged substances is largely reduced in water. We show by molecular dynamics simulation that the dielectric constant of water is decreased near the hydrophobic surface. We further show that the decrease in the dielectric constant is due to both the decreased water density and the reduced water dipole correlation in the direction perpendicular to the surface. We finally demonstrate that electrostatic interaction in water is actually strengthened near the hydrophobic surface.

Lessons from pressure denaturation of proteins

Although it is now relatively well understood how sequence defines and impacts global protein stability in specific structural contexts, the question of how sequence modulates the configurational landscape of proteins remains to be defined. Protein configurational equilibria are generally characterized by using various chemical denaturants or by changing temperature or pH. Another thermodynamic parameter which is less often used in such studies is high hydrostatic pressure. This review discusses the basis for pressure effects on protein structure and stability, and describes how the unique mechanisms of pressure-induced unfolding can provide unique insights into protein conformational landscapes.

Effects of Size and Functionalization on the Structure and Properties of Graphene Oxide Nanoflakes: An in Silico Investigation

Graphitic nanoparticles, specifically, graphene oxide (GO) nanoflakes, are of major interest in the field of nanotechnology, with potential applications ranging from drug delivery systems to energy storage devices. These applications are possible largely because of the properties imparted by various functional groups attached to the GO surface by relatively simple production methods compared to pristine graphene. We investigated how varying the size and oxidation of GO flakes can affect their structural and dynamic properties in an aqueous solution. The all-atom modeling of the GO nanoflakes of different sizes suggested that the curvature and roughness of relatively small (3 × 3 nm) GO flakes are not affected by their degree of oxidation. However, the larger (7 × 7 nm) flakes exhibited an increase in surface roughness as their oxidation increased. The analysis of water structure around the graphitic nanoparticles revealed that the degree of oxidation does not affect the water dipole orientations past the first hydration layer. Nevertheless, oxygen functionalization induced a well-structured first hydration layer, which manifested in identifiable hydrophobic and hydrophilic patches on GO. The detailed all-atom models of GO nanoflakes will guide a rational design of functional graphitic nanoparticles for biomedical and industrial applications.

Temperature Effects on Water-Mediated Interactions at the Nanoscale

We perform molecular dynamics simulations to study the effects of temperature on the water-mediated interactions between nanoscale apolar solutes. Specifically, we calculate the potential of mean force (PMF) between two graphene plates immersed in water at 240 ≤ T ≤ 400 K and P = 0.1 MPa. These are thermodynamic conditions relevant to cooling- and heating-induced protein denaturation. It is found that both cooling and heating tend to suppress the attraction, and ultimate collapse, of the graphene plates. However, the underlying role played by water upon heating and cooling is different. Isobaric heating reduces the strength and range of the interactions between the plates. Instead, isobaric cooling stabilizes the plates separations that can accommodate an integer number of water layers between the graphene plates. In particular, the energy barriers separating these plate separations increase linearly with 1/ T. We also explore the sensitivity of the plates PMF to the water model employed. In the case of the TIP4P/2005 model, water confined between the plates crystallizes into a defective bilayer ice at low temperatures, whereas in the case of the SPC/E model, water remains in the liquid state at same thermodynamic conditions. The effects of varying water-graphene interactions on the plates PMF are also studied.

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

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

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.

Peptide Solubility Limits: Backbone and Side-Chain Interactions

We calculate the solubility limit of pentapeptides in water by simulating the phase separation in an oversaturated aqueous solution. The solubility limit order followed by our model peptides (GGRGG > GGDGG > GGGGG > GGVGG > GGQGG > GGNGG > GGFGG) is found to be the same as that reported for amino acid monomers from experiment (R > D > G > V > Q > N > F). Investigation of dynamical properties of peptides shows that the higher the solubility of a peptide is, the lower the time spent by the peptide in the aggregated cluster is. We also demonstrate that fluctuations in conformation and hydration number of peptide in monomeric form are correlated with the solubility of the peptide. We considered energetic mechanisms and dynamical properties of interbackbone CO-CO and CO···HN interactions. Our results confirm that CO-CO interactions more than the interbackbone H-bonds are important in peptide self-assembly and association. Further, we find that the stability of H-bonded peptide pairs arises mainly from coexisting CO-CO and CO···HN interactions.

Density Fluctuation in Aqueous Solutions and Molecular Origin of Salting-Out Effect for CO2

Using molecular dynamics simulation, we studied the density fluctuations and cavity formation probabilities in aqueous solutions and their effect on the hydration of CO₂. With increasing salt concentration, we report an increased probability of observing a larger than the average number of species in the probe volume. Our energetic analyses indicate that the van der Waals and electrostatic interactions between CO₂ and aqueous solutions become more favorable with increasing salt concentration, favoring the solubility of CO₂ (salting in). However, due to the decreasing number of cavities forming when salt concentration is increased, the solubility of CO₂ decreases. The formation of cavities was found to be the primary control on the dissolution of gas, and is responsible for the observed CO₂ salting-out effect. Our results provide the fundamental understanding of the density fluctuation in aqueous solutions and the molecular origin of the salting-out effect for real gas.

Pressure-Dependence of Poly(N-isopropylacrylamide) Mesoglobule Formation in Aqueous Solution

Above their cloud point, aqueous solutions of the thermoresponsive polymer poly(N-isopropylacrylamide) (PNIPAM) form large mesoglobules. We have carried out very small-angle neutron scattering (VSANS with q = 0.21-2.3 × 10^-3 Å^-1) and Raman spectroscopy experiments on a 3 wt % PNIPAM solution in D₂O at atmospheric and elevated pressures (up to 113 MPa). Raman spectroscopy reveals that, at high pressure, the polymer is less dehydrated upon crossing the cloud point. VSANS shows that the mesoglobules are significantly larger and contain more D₂O than at atmospheric pressure. We conclude that the size of the mesoglobules and thus their growth process are closely related to the hydration state of PNIPAM.

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.