Statistical thermodynamics of aqueous solutions. I. Water structure, solutions with non-polar solutes, and hydrophobic interactions

A Mode-Coupling Model of Colloid Thermophoresis in Aqueous Systems: Temperature and Size Dependencies of the Soret Coefficient

Thermophoresis allows for the manipulation of colloids in systems containing a temperature gradient. A deep understanding of the phenomena at the molecular level allows for increased control and manipulation strategies. We developed a microscopic model revealing different coupling mechanisms for colloid thermophoresis under local thermodynamic equilibrium conditions. The model has been verified through comparison with a variety of previously published experimental data and shows good agreement across significantly different systems. We found five different temperature-dependent contributions to the Soret coefficient, two from bulk properties and three from interfacial interactions between the fluid medium and the colloid. Our analysis shows that the Soret coefficient for nanosized particles is governed by the competition between the electrostatic and hydration interfacial interactions, while bulk contributions become more pronounced for protein systems. This theory can be used as a guide to design thermophoretic transport, which is relevant for sensing, focusing, and separation at the microscale.

Simple Model of Liquid Water Dynamics

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

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

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

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

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

On the size, shape and energetics of the hydration shell around alkanes

A large number of clathrate-like cages have been proposed as the very first hydration shell of alkanes. The cages include canonical structures commonly found in clathrate hydrates and many others, not previously reported, derived from the carbon fullerene cavities. These structures have a rich and variegated form, which can adapt to the shape and conformation of the solute. They avoid "wasting" hydrogen bonds, while minimizing the volume cage and maximizing the solute-solvent van der Waals interactions. DFT/M06-2X and MP2 ab initio calculations give comparable structural and energetic results although the latter predicts slightly larger cages for a given solute. It is shown that the van der Waals interactions are substantial and the large exoenergetic values found for isobutane and cyclopentane provide an explanation for the surprising high melting points of related hydrates at room pressure. The encaging enthalpy for various hydrocarbons is similar to the enthalpy of solution measured at a temperature just above the melting point of aqueous hydrocarbon solutions, thus indicating that water molecules should not deviate too much from the configuration with O-H bonds tangentially oriented with respect to the solute surface. The computed trend differs from the enthalpy of solution measured at room temperature, thus the very first hydration shell departs, up to a certain degree, from the clathrate-like structures.

Influence of Ionic Strength on Hydrophobic Interactions in Water: Dependence on Solute Size and Shape

Hydrophobicity is a phenomenon of great importance in biology, chemistry, and biochemistry. It is defined as the interaction between nonpolar molecules or groups in water and their low solubility. Hydrophobic interactions affect many processes in water, for example, complexation, surfactant aggregation, and coagulation. These interactions play a pivotal role in the formation and stability of proteins or biological membranes. In the present study, we assessed the effect of ionic strength, solute size, and shape on hydrophobic interactions between pairs of nonpolar particles. Pairs of methane, neopentane, adamantane, fullerene, ethane, propane, butane, hexane, octane, and decane were simulated by molecular dynamics in AMBER 16.0 force field. As a solvent, TIP3P and TIP4PEW water models were used. Potential of mean force (PMF) plots of these dimers were determined at four values of ionic strength, 0, 0.04, 0.08, and 0.40 mol/dm³, to observe its impact on hydrophobic interactions. The characteristic shape of PMFs with three extrema (contact minimum, solvent-separated minimum, and desolvation maximum) was observed for most of the compounds for hydrophobic interactions. Ionic strength affected hydrophobic interactions. We observed a tendency to deepen contact minima with an increase in ionic strength value in the case of spherical and spheroidal molecules. Additionally, two-dimensional distribution functions describing water density and average number of hydrogen bonds between water molecules were calculated in both water models for adamantane and hexane. It was observed that the density of water did not significantly change with the increase in ionic strength, but the average number of hydrogen bonds changed. The latter tendency strongly depends on the water model used for simulations.

A Theoretical Study of the Hydration of Methane, from the Aqueous Solution to the sI Hydrate-Liquid Water-Gas Coexistence

Monte Carlo and molecular dynamics simulations were done with three recent water models TIP4P/2005 (Transferable Intermolecular Potential with 4 Points/2005), TIP4P/Ice (Transferable Intermolecular Potential with 4 Points/ Ice) and TIP4Q (Transferable Intermolecular Potential with 4 charges) combined with two models for methane: an all-atom one OPLS-AA (Optimal Parametrization for the Liquid State) and a united-atom one (UA); a correction for the C–O interaction was applied to the latter and used in a third set of simulations. The models were validated by comparison to experimental values of the free energy of hydration at 280, 300, 330 and 370 K, all under a pressure of 1 bar, and to the experimental radial distribution functions at 277, 283 and 291 K, under a pressure of 145 bar. Regardless of the combination rules used for σ_C,O, good agreement was found, except when the correction to the UA model was applied. Thus, further simulations of the sI hydrate were performed with the united-atom model to compare the thermal expansivity to the experiment. A final set of simulations was done with the UA methane model and the three water models, to study the sI hydrate-liquid water-gas coexistence at 80, 230 and 400 bar. The melting temperatures were compared to the experimental values. The results show the need to perform simulations with various different models to attain a reliable and robust molecular image of the systems of interest.

My 65 years in protein chemistry

This is a tour of a physical chemist through 65 years of protein chemistry from the time when emphasis was placed on the determination of the size and shape of the protein molecule as a colloidal particle, with an early breakthrough by James Sumner, followed by Linus Pauling and Fred Sanger, that a protein was a real molecule, albeit a macromolecule. It deals with the recognition of the nature and importance of hydrogen bonds and hydrophobic interactions in determining the structure, properties, and biological function of proteins until the present acquisition of an understanding of the structure, thermodynamics, and folding pathways from a linear array of amino acids to a biological entity. Along the way, with a combination of experiment and theoretical interpretation, a mechanism was elucidated for the thrombin-induced conversion of fibrinogen to a fibrin blood clot and for the oxidative-folding pathways of ribonuclease A. Before the atomic structure of a protein molecule was determined by x-ray diffraction or nuclear magnetic resonance spectroscopy, experimental studies of the fundamental interactions underlying protein structure led to several distance constraints which motivated the theoretical approach to determine protein structure, and culminated in the Empirical Conformational Energy Program for Peptides (ECEPP), an all-atom force field, with which the structures of fibrous collagen-like proteins and the 46-residue globular staphylococcal protein A were determined. To undertake the study of larger globular proteins, a physics-based coarse-grained UNited-RESidue (UNRES) force field was developed, and applied to the protein-folding problem in terms of structure, thermodynamics, dynamics, and folding pathways. Initially, single-chain and, ultimately, multiple-chain proteins were examined, and the methodology was extended to protein-protein interactions and to nucleic acids and to protein-nucleic acid interactions. The ultimate results led to an understanding of a variety of biological processes underlying natural and disease phenomena.

Gibbs free energy of liquid water derived from infrared measurements

A completely new set of IR bands of liquid water from 4 cm⁻¹ to 4000 cm⁻¹ is studied from spectroscopic and thermodynamic viewpoints over a large thermal range, evidencing the so-called isosbestic points on the different absorption bands.

Solvation theory to provide a molecular interpretation of the hydrophobic entropy loss of noble-gas hydration

An equation for the chemical potential of a dilute aqueous solution of noble gases is derived in terms of energies, force and torque magnitudes, and solute and water coordination numbers, quantities which are all measured from an equilibrium molecular dynamics simulation. Also derived are equations for the Gibbs free energy, enthalpy and entropy of hydration for the Henry's law process, the Ostwald process, and a third proposed process going from an arbitrary concentration in the gas phase to the equivalent mole fraction in aqueous solution which has simpler expressions for the enthalpy and entropy changes. Good agreement with experimental hydration free energies is obtained in the TIP4P and SPC/E water models although the solute's force field appears to affect the enthalpies and entropies obtained. In contrast to other methods, the approach gives a complete breakdown of the entropy for every degree of freedom and makes possible a direct structural interpretation of the well-known entropy loss accompanying the hydrophobic hydration of small non-polar molecules under ambient conditions. The noble-gas solutes experience only a small reduction in their vibrational entropy, with larger solutes experiencing a greater loss. The vibrational and librational entropy components of water actually increase but only marginally, negating any idea of water confinement. The term that contributes the most to the hydrophobic entropy loss is found to be water's orientational term which quantifies the number of orientational minima per water molecule and how many ways the whole hydrogen-bond network can form. These findings help resolve contradictory deductions from experiments that water structure around non-polar solutes is similar to bulk water in some ways but different in others. That the entropy loss lies in water's rotational entropy contrasts with other claims that it largely lies in water's translational entropy, but this apparent discrepancy arises because of different coordinate definitions and reference frames used to define the entropy terms.

The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method

While the Stokes-Einstein (SE) equation predicts that the diffusion coefficient of a solute will be inversely proportional to the viscosity of the solvent, this relation is commonly known to fail for solutes, which are the same size or smaller than the solvent. Multiple researchers have reported that for small solutes, the diffusion coefficient is inversely proportional to the viscosity to a fractional power, and that solutes actually diffuse faster than SE predicts. For other solvent systems, attractive solute-solvent interactions, such as hydrogen bonding, are known to retard the diffusion of a solute. Some researchers have interpreted the slower diffusion due to hydrogen bonding as resulting from the effective diffusion of a larger complex of a solute and solvent molecules. We have developed and used a novel micropipette technique, which can form and hold a single microdroplet of water while it dissolves in a diffusion controlled environment into the solvent. This method has been used to examine the diffusion of water in both n-alkanes and n-alcohols. It was found that the polar solute water, diffusing in a solvent with which it cannot hydrogen bond, closely resembles small nonpolar solutes such as xenon and krypton diffusing in n-alkanes, with diffusion coefficients ranging from 12.5x10(-5) cm(2)/s for water in n-pentane to 1.15x10(-5) cm(2)/s for water in hexadecane. Diffusion coefficients were found to be inversely proportional to viscosity to a fractional power, and diffusion coefficients were faster than SE predicts. For water diffusing in a solvent (n-alcohols) with which it can hydrogen bond, diffusion coefficient values ranged from 1.75x10(-5) cm(2)/s in n-methanol to 0.364x10(-5) cm(2)/s in n-octanol, and diffusion was slower than an alkane of corresponding viscosity. We find no evidence for solute-solvent complex diffusion. Rather, it is possible that the small solute water may be retarded by relatively longer residence times (compared to non-H-bonding solvents) as it moves through the liquid.

A single-molecule perspective on the role of solvent hydrogen bonds in protein folding and chemical reactions

We present an array of force spectroscopy experiments that aim to identify the role of solvent hydrogen bonds in protein folding and chemical reactions at the single-molecule level. In our experiments we control the strength of hydrogen bonds in the solvent environment by substituting water (H(2)O) with deuterium oxide (D(2)O). Using a combination of force protocols, we demonstrate that protein unfolding, protein collapse, protein folding and a chemical reaction are affected in different ways by substituting H(2)O with D(2)O. We find that D(2)O molecules form an integral part of the unfolding transition structure of the immunoglobulin module of human cardiac titin, I27. Strikingly, we find that D(2)O is a worse solvent than H(2)O for the protein I27, in direct contrast with the behaviour of simple hydrocarbons. We measure the effect of substituting H(2)O with D(2)O on the force dependent rate of reduction of a disulphide bond engineered within a single protein. Altogether, these experiments provide new information on the nature of the underlying interactions in protein folding and chemical reactions and demonstrate the power of single-molecule techniques to identify the changes induced by a small change in hydrogen bond strength.

From helix-coil transitions to protein folding

An evolution of procedures to simulate protein structure and folding pathways is described. From an initial focus on the helix-coil transition and on hydrogen-bonding and hydrophobic interactions, our original attempts to determine protein structure and folding pathways were based on an experimental approach. Experiments on the oxidative folding of reduced bovine pancreatic ribonuclease A (RNase A) led to a mechanism by which the molecule folded to the native structure by a minimum of four different pathways. The experiments with RNase A were followed by development of a molecular mechanics approach, first, making use of global optimization procedures and then with molecular dynamics (MD), evolving from an all-atom to a united-residue model. This hierarchical MD approach facilitated probing of the folding trajectory to longer time scales than with all-atom MD, and hence led to the determination of complete folding trajectories, thus far for a protein containing as many as 75 amino acid residues. With increasing refinement of the computational procedures, the computed results are coming closer to experimental observations, providing an understanding as to how physics directs the folding process.

Theory for the solvation of nonpolar solutes in water

We recently developed an angle-dependent Wertheim integral equation theory (IET) of the Mercedes-Benz (MB) model of pure water [Silverstein et al., J. Am. Chem. Soc. 120, 3166 (1998)]. Our approach treats explicitly the coupled orientational constraints within water molecules. The analytical theory offers the advantage of being less computationally expensive than Monte Carlo simulations by two orders of magnitude. Here we apply the angle-dependent IET to studying the hydrophobic effect, the transfer of a nonpolar solute into MB water. We find that the theory reproduces the Monte Carlo results qualitatively for cold water and quantitatively for hot water.

Effects of Cyclodextrins on Drug Delivery Through Biological Membranes

Cyclodextrins have proven themselves to be useful functional excipients. Cyclodextrin derivatives can be hydrophilic or relatively lipophilic based on their substitution and these properties can give insight into their ability to act as permeability enhancers. Lipophilic cyclodextrins such as the methylated derivatives are thought to increase drug flux by altering barrier properties of the membrane through component extraction or fluidization. The hydrophilic cyclodextrin family also modulate drug flux through membranes but via different mechanisms. The current effort seeks to provide various explanations for these observations based on interactions of hydrophilic cyclodextrins with the unstirred water layer that separates the bulk media from biological membranes such as the gastric mucosa, cornea and reproductive tract. Theories on the serial nature of resistances to drug flux are used to explain why hydrophilic cyclodextrins can enhance drug uptake in some situation (i.e., for lipophilic material) but not in others. In addition, the nature of secondary equilibria and competition between cyclodextrins and rheologically important biopolymers such as mucin are assessed to give a complete picture of the effect of these starch derivatives. This information can be useful not only in understanding the actions of cyclodextrin but also in expanding their application and uses.

Potential of Mean Force of Hydrophobic Association: Dependence on Solute Size

The potentials of mean force (PMFs) were determined for systems involving formation of nonpolar dimers composed of methane, ethane, propane, isobutane, and neopentane, respectively, in water, using the TIP3P water model, and in vacuo. A series of umbrella-sampling molecular dynamics simulations with the AMBER force field was carried out for each pair in either water or in vacuo. The PMFs were calculated by using the weighted histogram analysis method (WHAM). The shape of the PMFs for dimers of all five nonpolar molecules is characteristic of hydrophobic interactions with contact and solvent-separated minima and desolvation maxima. The positions of all these minima and maxima change with the size of the nonpolar molecule, that is, for larger molecules they shift toward larger distances. The PMF of the neopentane dimer is similar to those of other small nonpolar molecules studied in this work, and hence the neopentane dimer is too small to be treated as a nanoscale hydrophobic object. The solvent contribution to the PMF was also computed by subtracting the PMF determined in vacuo from the PMF in explicit solvent. The molecular surface area model correctly describes the solvent contribution to the PMF together with the changes of the height and positions of the desolvation barrier for all dimers investigated. The water molecules in the first solvation sphere of the dimer are more ordered compared to bulk water, with their dipole moments pointing away from the surface of the dimer. The average number of hydrogen bonds per water molecule in this first hydration shell is smaller compared to that in bulk water, which can be explained by coordination of water molecules to the hydrocarbon surface. In the second hydration shell, the average number of hydrogen bonds is greater compared to bulk water, which can be explained by increased ordering of water from the first hydration shell; the net effect is more efficient hydrogen bonding between the water molecules in the first and second hydration shells.

Water properties and potential of mean force for hydrophobic interactions of methane and nanoscopic pockets studied by computer simulations

We consider model systems consisting of a methane molecule and hemispherical pockets of subnanometer radii whose walls are made of hydrophobic material. The potential of mean force for process of translocation of the methane molecule from bulk water into the pockets' interior is obtained, based on an explicit solvent molecular dynamics simulations. Accompanying changes in water density around the interacting objects and spatial distribution of solvent's potential energy are analyzed, allowing for interpretation of details of hydrophobic interactions in relation to hydrophobic hydration properties. Applicability of surface area-based models of hydrophobic effect for systems of interest is also investigated. A total work for the translocation process is not dependent on pocket's size, indicating that pocket desolvation has little contribution to free energy changes, which is consistent with the observation that solvent density is significantly reduced inside "unperturbed" pockets. Substantial solvent effects are shown to have a longer range than in case of a well investigated methane pair. A desolvation barrier is present in a smaller pocket system but disappears in the larger one, suggesting that a form of a "hydrophobic collapse" is observed.

Water properties inside nanoscopic hydrophobic pocket studied by computer simulations

The structure and dynamics of water in the vicinity of the hemispherical hydrophobic pocket of 8 A radius were examined via molecular dynamics simulations in NVT ensemble. Density, hydrogen bonding properties, and residence times of water molecules were projected on two-dimensional planes providing a spatial description of water behavior. We found that the average water density is significantly depleted relative to bulk value. A detailed analysis of pocket occupancy revealed fluctuations between states of completely empty pocket and a pocket filled with a bulklike fluid, which seem to result from collective behavior of water molecules. Free energy differences accompanying these fluctuations are rather small, suggesting that the given pocket radius is close to the critical one for transition between gas and liquid phases in the considered system. We show that the situation is different in the case of a simple Lennard-Jones fluid. These results indicate that changing the surface curvature from flat to concave may lead to qualitative difference in water behavior in its vicinity. We think that our studies may also put some light on binding site desolvation process which is necessary to understand to make correct predictions of binding energies.

Hydrophobic Hydration in an Orientational Lattice Model

To shed light on the microscopic mechanism of hydrophobic hydration, we study a simplified lattice model for water solutions in which the orientational nature of hydrogen bonding as well as the degeneracy related to proton distribution are taken into account. Miscibility properties of the model are looked at for both polar (hydrogen bonding) and nonpolar (non-hydrogen bonding) solutes. A quasichemical solution for the pure system is reviewed and extended to include the different kinds of solute. A Monte Carlo study of our model yields a novel feature for the local structure of the hydration layer: energy correlation relaxation times for solvation water are larger than the corresponding relaxation times for bulk water. This result suggests the presence of ordering of water particles in the first hydration shell. A nonassociating model solvent, represented by a lattice gas, presents opposite behavior, indicating that this effect is a result of the directionality of the interaction. In presence of polar solutes, we find an ordered mixed pseudophase at low temperatures, indicating the possibility of closed loops of immiscibility.

Direct Measure of the Hydration Number of Aqueous Methane

A hydration number of 20 has been measured for aqueous CH4 in the temperature range 273-298 K on the basis of the simultaneous observation of the 13C isotropic resonance lines of CH4 in both aqueous solution and the dodecahedral cage of CH4 structure I hydrate. Additional experimental evidence and analysis reported in this paper suggest that the dominant aqueous hydration number of methane is 20.