Osmotic Second Virial Coefficient of Methane in Water

Interactions between Water and a Hydrophobic Polymer

To investigate the mechanisms of interactions between a hydrophobic polymer and water, molecular dynamics calculations and Raman spectroscopic measurements of cis-1,4-polyisoprene (PI)-water systems were performed. The results show that PI in water undergoes a coil-globule transition at around 248 K. The transition is attributed to changes in the density and diffusivity of water. The volume expansion of the supercooled liquid water induces the coil structure of PI. The phase separation of PI from water with an increase in the self-diffusion coefficient of water molecules results in the globule structure of PI. The self-diffusion coefficient of free water with PI is larger than that of pure water because PI has an effect to decrease the hydrogen-bonding strength of water. The result suggests that the effects of the coexisting water are important factors governing the physical and chemical properties of hydrophobic polymers.

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

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

Osmotic Force Balance Evaluation of Aqueous Electrolyte Osmotic Pressures and Chemical Potentials

Concentrated aqueous salt solutions are ubiquitous in problems of biological and environmental relevance. The development of accurate force fields that capture the interactions between dissolved species in solution is crucial to simulating these systems to gain molecular insights into the underlying processes under saline conditions. The osmotic pressure is a relatively simple thermodynamic property connecting the experimental and simulation measurements of the associative properties of the ions in solution. Milner [C. Gillespie and S. T. Milner, Soft Matter, 16, 9816 (2020)] proposed a simulation approach to evaluate the osmotic pressures of salts in solution by applying a restraint potential to the ions alone in solution and determining the resulting pressure required to balance that potential, referred to here as the osmotic force balance. Here, we expand Milner's approach, demonstrating that the chemical potentials of the salts in solution as a function of concentration can be fitted to the concentration profiles determined from simulation, additionally providing an analytical expression for the osmotic pressure. This approach is used to determine the osmotic pressures of 15 alkali halide salts in water from simulations. The cross interactions between cations and anions in solution are subsequently optimized to capture their experimental osmotic pressures.

Determination of specific and non-specific protein-protein interactions for beta-lactoglobulin by analytical ultracentrifugation and membrane osmometry experiments

Protein-protein interactions are essential for the understanding of biological processes. Specific protein aggregation is an important aspect for many biological systems. In particular, electrostatic interactions play the key role for protein-protein interactions, as many amino acids have pH-dependent charge states. Moreover, protein dissociation is directly related to the solution pH, ionic strength, temperature and protein concentration. The subtle interplay between different specific and non-specific interactions is demonstrated for beta-lactoglobulin (BLG) with a focus on low salt concentrations, thus mimicking technically relevant processing conditions. BLG is a well-characterized model system, proven to attain its monomer-dimer equilibrium strongly dependent upon the pH of the solution. In this manuscript, we present a unique combination of analytical ultracentrifugation and membrane osmometry experiments, which quantifies specific and non-specific interactions, i.e. in terms of the dimer dissociation constants and the second osmotic virial coefficient, at pH 3 and 7 and sodium chloride concentrations of 10 mM and 100 mM. This provides direct insight to protein-protein interactions for a system with a concentration-dependent monomer-dimer equilibrium. Moreover, using a coarse-grained extended DLVO model in combination with molecular dynamics simulations, we quantify non-specific monomer-monomer, monomer-dimer and dimer-dimer interactions as well as the binding free energy of BLG dimerization from theoretical calculations. The experimentally determined interactions are shown to be mainly governed by electrostatic interactions and further agree with free energy calculations. Our experimental protocol aims to determine non-specific and specific interactions for a dynamically interacting system and provides an understanding of protein-protein interactions for BLG at low salt concentrations.

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

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

Temperature induced change of TMAO effects on hydrophobic hydration

The effect of trimethylamine-N-oxide (TMAO) on hydrophobic solvation and hydrophobic interactions of methane has been studied with Molecular Dynamics simulations in the temperature range between 280 and 370 K at 1 bar ambient pressure. We observe a temperature transition in the effect of TMAO on the aqueous solubility of methane. At low temperature (280 K), methane is preferentially hydrated, causing TMAO to reduce its solubility in water, while above 320 K, methane preferentially interacts with TMAO, causing TMAO to promote its solubility in water. Based on a statistical-mechanical analysis of the excess chemical potential of methane, we find that the reversible work of creating a repulsive methane cavity opposes the solubility of methane in TMAO/water solution more than in pure water. Below 320 K, this solvent-excluded volume effect overcompensates the contribution of methane–TMAO van der Waals interactions, which promote the solvation of methane and are observed at all temperatures. These van der Waals interactions with the methyl groups of TMAO tip the balance above 320 K where the effect of TMAO on solvent-excluded volume is smaller. We furthermore find that the effective attraction between dissolved methane solutes increases with the increasing TMAO concentration. This observation correlates with a reduction in the methane solubility below 320 K but with an increase in methane solubility at higher temperatures.

Evidence of Many-Body Interactions in the Virial Coefficients of Polyelectrolyte Gels

Simulation studies of aqueous polymer solutions, and heuristic arguments by De Gennes for aqueous polyethylene oxide polymer solutions, have suggested that many-body interactions can give rise to the ‘anomalous’ situation in which the second osmotic virial coefficient is positive, while the third virial coefficient is negative. This phenomenon was later confirmed in analytic calculations of the phase behavior and the osmotic pressure of complex fluids exhibiting cooperative self-assembly into extended dynamic polymeric structures by Dudowicz et al. In the present study, we experimentally confirm the occurrence of this osmotic virial sign inversion phenomenon for several highly charged model polyelectrolyte gels (poly(acrylic acid), poly(styrene sulfonate), DNA, hyaluronic acid), where the virial coefficients are deduced from osmotic pressure measurements. Our observations qualitatively accord with experimental and simulation studies indicating that polyelectrolyte materials exhibit supramolecular assembly in solution, another symptomatic property of fluids exhibiting many-body interactions. We also find that the inversion in the variation of the second (A₂) and third (A₂) virial coefficients upon approach to phase separation does not occur in uncharged poly(vinyl acetate) gels. Finally, we briefly discuss the estimation of the osmotic compressibility of swollen polyelectrolyte gels from neutron scattering measurements as an alternative to direct, time-consuming and meticulous osmotic pressure measurements. We conclude by summarizing some general trends and suggesting future research directions of natural and synthetic polyelectrolyte hydrogels.

Water-mediated interactions destabilize proteins

Proteins are folded to avoid exposure of the nonpolar groups to water because water‐mediated interactions between nonpolar groups are a promising factor in the thermodynamic stabilities of proteins—which is a well‐accepted view as one of the unique effects of hydrophobic interactions. This article poses a critical question for this classical view by conducting an accurate solvation free‐energy calculation for a thermodynamic cycle of a protein folding using a liquid‐state density functional theory. Here, the solvation‐free energy for a leucine zipper formation was examined in the coiled‐coil protein GCN4‐p1, a typical model for hydrophobic interactions, which demonstrated that water‐mediated interactions were unfavorable for the association of nonpolar groups in the native state, while the dispersion forces between them were, instead, responsible for the association. Furthermore, the present analysis well predicted the isolated helical state stabilized by pressure, which was previously observed in an experiment. We reviewed the problems in the classical concept and semiempirical presumption that the energetic cost of the hydration of nonpolar groups is a driving force of folding.

Reduction of water-mediated repulsion drives poly(N-vinylcaprolactam) collapse upon heating

Thermo-sensitive aqueous polymers undergo a coil-to-globule transition on heating, with drastic chemical and structural changes. We performed molecular dynamics simulations for PVCL in water to study the driving forces for the polymer's collapse.

Hydration-Shell Vibrational Spectroscopy

Hydration-shell vibrational spectroscopy provides an experimental window into solute-induced water structure changes that mediate aqueous folding, binding, and self-assembly. Decomposition of measured Raman and infrared (IR) spectra of aqueous solutions using multivariate curve resolution (MCR) and related methods may be used to obtain solute-correlated spectra revealing solute-induced perturbations of water structure, such as changes in water hydrogen-bond strength, tetrahedral order, and the presence of dangling (non-hydrogen-bonded) OH groups. More generally, vibrational-MCR may be applied to both aqueous and nonaqueous solutions, including multicomponent mixtures, to quantify solvent-mediated interactions between oily, polar, and ionic solutes, in both dilute and crowded fluids. Combining vibrational-MCR with emerging theoretical modeling strategies promises synergetic advances in the predictive understanding of multiscale self-assembly processes of both biological and technological interest.

Connections between the Anomalous Volumetric Properties of Alcohols in Aqueous Solution and the Volume of Hydrophobic Association

The partial molar volumes of alcohols in water exhibit a non-monotonic dependence on concentration at room temperature, initially decreasing with increasing concentration before passing through a minimum and rising to the pure liquid plateau. This anomalous behavior is associated with hydrophobic interactions. We report molecular simulations of short chain alcohols and alkanes in water to examine the volumetric properties of these mixtures at infinite dilution over a range of temperatures. Our simulations find this anomaly disappears at a crossover temperature, above which the solute volume only varies monotonically with concentration. A Voronoi volume analysis of solution configurations finds that solutes in clusters take up less space than individual solutes at low temperature and more space at elevated temperatures. These changes in cluster volumes are subsequently shown to correlate with the derivative of the solute partial molar volume with respect to solute concentration. The changes in solute volume upon nonpolar solute association impact the response of molecular-scale hydrophobic interactions for assembly with increasing pressure.

Hydrophobicity Varying with Temperature, Pressure, and Salt Concentration

Temperature-, pressure-, and salt-concentration-induced variations in the solubility of small nonpolar solutes in aqueous solution and the corresponding variations in the solvent-induced pair attraction between such solute molecules are investigated. The variations in the solvation free energy of a solute and those in the solvent-induced pair attraction are well reproduced by a mean-field approximation in which the repulsive cores of solute molecules are treated as hard spheres and the mean-field energy of a solute molecule is taken to be the average potential energy that the solute molecule feels in solution. The mechanisms of variation in the solvation free energy and those of variation in the solvent-induced pair potential, with increasing temperature, pressure, and salt concentration, are clarified. Correlations between the solvation free energy and the solvent-induced pair potential at a contact distance in temperature, pressure, and salt concentration variations are near linear in any mode of variation, but the slope of the linear relation is dependent on the mode of variation and is determined by a ratio of the solvation thermodynamic quantities characteristic of each mode of variation.

Statistical Analyses of Hydrophobic Interactions: A Mini-Review

This review focuses on the striking recent progress in solving for hydrophobic interactions between small inert molecules. We discuss several new understandings. First, the inverse temperature phenomenology of hydrophobic interactions, i.e., strengthening of hydrophobic bonds with increasing temperature, is decisively exhibited by hydrophobic interactions between atomic-scale hard sphere solutes in water. Second, inclusion of attractive interactions associated with atomic-size hydrophobic reference cases leads to substantial, nontrivial corrections to reference results for purely repulsive solutes. Hydrophobic bonds are weakened by adding solute dispersion forces to treatment of reference cases. The classic statistical mechanical theory for those corrections is not accurate in this application, but molecular quasi-chemical theory shows promise. Finally, because of the masking roles of excluded volume and attractive interactions, comparisons that do not discriminate the different possibilities face an interpretive danger.

Liquid-liquid phase separation of N-isopropylpropionamide aqueous solutions above the lower critical solution temperature

We investigate driving forces of the liquid–liquid phase separation of N-isopropylpropionamide (NiPPA) aqueous solutions above the lower critical solution temperature using molecular dynamics simulations. Spontaneous phase separations of the model aqueous solution with a modified OPLS-AA force field are observed above the experimentally determined cloud point. The destabilization toward the phase separation is confirmed by temperature dependence of the long-wavelength limit of the concentration-concentration structure factor, the dominant component of which is found to be an increasing effective attraction between NiPPA molecules. At varying temperatures, the potentials of mean force (PMFs) between a pair of NiPPA molecules at infinite dilution are obtained and decomposed into the nonpolar and Coulombic contributions. The nonpolar contribution, arising essentially from molecular volume, promotes association of NiPPA molecules with increasing temperature while the Coulombic one antagonizes the association. Thus, our analysis leads to a conclusion that the driving force of thermally induced aggregation of NiPPA molecules is the temperature dependence of the nonpolar contribution in PMF between NiPPA molecules, not the temperature dependence of the number or strength of hydrogen bonds between NiPPA and water molecules.

Cononsolvency behavior of hydrophobes in water + methanol mixtures

The molecular origin of cononsolvency behavior is explored using molecular dynamics simulations.

Driving forces for the pressure-induced aggregation of poly(N-isopropylacrylamide) in water

Driving forces for the pressure-induced aggregation of poly(N-isopropylacrylamide) in water are discussed.

McMillan-Mayer theory of solutions revisited: simplifications and extensions

McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium statistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to one with an effectively solute-only form, by integrating out the solvent degrees of freedom. The total effective solute potential in the effective solute grand partition function can be decomposed into components which are potentials of mean force for isolated groups of one, two, three, etc., solute molecules. Second, from the first result, now assuming low solute concentration, MM derived an expansion for the osmotic pressure in powers of the solute concentration, in complete analogy with the virial expansion of gas pressure in powers of the density at low density. The molecular expressions found for the osmotic virial coefficients have exactly the same form as the corresponding gas virial coefficients, with potentials of mean force replacing vacuum potentials. In this paper, we restrict ourselves to binary liquid solutions with solute species A and solvent species B and do three things: (a) By working with a semi-grand canonical ensemble (grand with respect to solvent only) instead of the grand canonical ensemble used by MM, and avoiding graphical methods, we have greatly simplified the derivation of the first MM result, (b) by using a simple nongraphical method developed by van Kampen for gases, we have greatly simplified the derivation of the second MM result, i.e., the osmotic pressure virial expansion; as a by-product, we show the precise relation between MM theory and Widom potential distribution theory, and (c) we have extended MM theory by deriving virial expansions for other solution properties such as the enthalpy of mixing. The latter expansion is proving useful in analyzing ongoing isothermal titration calorimetry experiments with which we are involved. For the enthalpy virial expansion, we have also changed independent variables from semi-grand canonical, i.e., fixed {N(A), μ(B), V, T}, to those relevant to the experiment, i.e., fixed {N(A), N(B), p, T}, where μ denotes chemical potential, N the number of molecules, V the volume, p the pressure, and T the temperature.

Physicochemical nature of interfaces controlling ferredoxin NADP(+) reductase activity through its interprotein interactions with ferredoxin

Although acidic residues of ferredoxin (Fd) are known to be essential for activities of various Fd-dependent enzymes, including ferredoxin NADP(+) reductase (FNR) and sulfite reductase (SiR), through electrostatic interactions with basic residues of partner enzymes, non-electrostatic contributions such as hydrophobic forces remain largely unknown. We herein demonstrated that intermolecular hydrophobic and charge-charge interactions between Fd and enzymes were both critical for enzymatic activity. Systematic site-directed mutagenesis, which altered physicochemical properties of residues on the interfaces of Fd for FNR /SiR, revealed various changes in activities of both enzymes. The replacement of serine 43 of Fd to a hydrophobic residue (S43W) and charged residue (S43D) increased and decreased FNR activity, respectively, while S43W showed significantly lower SiR activity without affecting SiR activity by S43D, suggesting that hydrophobic and electrostatic interprotein forces affected FNR activity. Enzyme kinetics revealed that changes in FNR activity by mutating Fd correlated with Km, but not with kcat or activation energy, indicating that interprotein interactions determined FNR activity. Calorimetry-based binding thermodynamics between Fd and FNR showed different binding modes of FNR to wild-type, S43W, or S43D, which were controlled by enthalpy and entropy, as shown by the driving force plot. Residue-based NMR spectroscopy of (15)N FNR with Fds also revealed distinct binding modes of each complex based on different directions of NMR peak shifts with similar overall chemical shift differences. We proposed that subtle adjustments in both hydrophobic and electrostatic forces were critical for enzymatic activity, and these results may be applicable to protein-based electron transfer systems.

Hydrophobic Ambivalence: Teetering on the Edge of Randomness

Processes ranging from oil-water phase separation to the formation of solid clathrate hydrates send mixed messages regarding whether oil molecules hate or love to be surrounded by water. Recent experimental and theoretical results help decipher these mixed messages by illuminating the conditions under which the stability of a hydrophobic contact is expected to exceed thermal energy fluctuations - thus facilitating hydrophobic self-assembly and the emergence of structure from randomness. Important open questions remain regarding the dependence of hydrophobic interactions on molecular size and temperature, as well as the balance of direct and water-mediated interactions.

Effect of hydrostatic pressure on gas solubilization in micelles

Molecular dynamics simulations of anionic sodium decylsulfate and nonionic pentaethylene glycol monodecyl ether micelles in water have been performed to examine the impact of hydrostatic pressure on argon solubilization as a function of pressure. The potential-of-mean force between the micelles and argon demonstrates that nonpolar gases are attracted to the interiors of both micelles. The affinity of argon for micelle interiors, however, decreases with increasing pressure as a result of the comparatively higher molar volume of argon inside assemblies. We evaluate solubility enhancement coefficients, which describe the drop in the solute chemical potential as a function of the micellized surfactant concentration, to quantify the impact of micellization on gas solubilization. While argon is similarly attracted to the hydrophobic cores of both micelles, the gas is more effectively sequestered within nonionic micelles compared with anionic micelles as a result of salting out by charged head groups and accompanying counterions. The solubility enhancement coefficients of both micelles decrease with increasing pressure, reflecting the changing forces observed in the potentials-of-mean force. An analytical liquid drop model is proposed to describe the pressure dependence of argon solubilization within micelles that captures the simulation solubility enhancement coefficients after fitting an effective micelle radius for each surfactant.

Contacts Between Alcohols in Water Are Random Rather than Hydrophobic

Given the importance of water-mediated hydrophobic interactions in a wide range of biological and synthetic self-assembly processes, it is remarkable that both the sign and the magnitude of the hydrophobic interactions between simple amphiphiles, such as alcohols, remain unresolved. To address this question, we have performed Raman hydration-shell vibrational spectroscopy and polarization-resolved femtosecond infrared experiments, as well as random mixing and molecular dynamics simulations. Our results indicate that there are no more hydrophobic contacts in aqueous solutions of alcohols ranging from methanol to tertiary butyl alcohol than in random mixtures of the same concentration. This implies that the interaction between small hydrophobic groups is weaker than thermal energy fluctuations. Thus, the corresponding water-mediated hydrophobic interaction must be repulsive, with a magnitude sufficient to negate the attractive direct van der Waals interaction between the hydrophobic groups.

Molecular-scale hydrophobic interactions between hard-sphere reference solutes are attractive and endothermic

The osmotic second virial coefficients, B2, for atomic-sized hard spheres in water are attractive (B2 < 0) and become more attractive with increasing temperature (ΔB2/ΔT < 0) in the temperature range 300 K ≤ T ≤ 360 K. Thus, these hydrophobic interactions are attractive and endothermic at moderate temperatures. Hydrophobic interactions between atomic-sized hard spheres in water are more attractive than predicted by the available statistical mechanical theory. These results constitute an initial step toward detailed molecular theory of additional intermolecular interaction features, specifically, attractive interactions associated with hydrophobic solutes.