Potential of mean force between hydrophobic solutes in the Jagla model of water and implications for cold denaturation of proteins

Using the Jagla model potential we calculate the potential of mean force (PMF) between hard sphere solutes immersed in a liquid displaying water-like properties. Consistent estimates of the PMF are obtained by (a) umbrella sampling, (b) calculating the work done by the mean force acting on the hard spheres as a function of their separation, and (c) determining the position dependent chemical potential after calculating the void space in the liquid. We calculate the PMF for an isobar along which cold denaturation of a model protein has previously been reported. We find that the PMF at contact varies non-monotonically, which is consistent with the observed cold denaturation. The Henry constant also varies non-monotonically with temperature. We find, on the other hand, that a second (solvent separated) minimum of the PMF becomes deeper as temperature decreases. We calculate the solvent-solvent pair correlation functions for solvents near the solute and in the bulk, and show that, as temperature decreases, the two pair correlation functions become indistinguishable, suggesting that the perturbation of solvent structure by the solute diminishes as temperature decreases. The solvent-solute pair correlation function at contact grows as the temperature decreases. We calculate the cavity correlation function and show the development of a solvent-separated peak upon decrease of temperature. These observations together suggest that cold denaturation occurs when the solvent penetrates between hydrophobic solutes in configurations with favorable free energy. Our results thus suggest that cold denatured proteins are structured and that cold denaturation arises from strong solvent-solute interactions, rather than from entropic considerations as in heat denaturation.     

A study of the phase behavior of a simple model of chiral molecules and enantiomeric mixtures

We present a study of the solid-fluid and solid-solid phase equilibrium for molecular models representative of chiral molecules and enantiomeric mixtures. The models consist of four hard sphere interaction sites of different diameters in a tetrahedral arrangement with the fifth hard sphere interaction site at the center of the tetrahedron. The volumetric properties and free energies of the pure enantiomers and binary mixtures were calculated in both fluid and solid phases using isobaric Monte Carlo simulations. The models exhibit essentially ideal solution behavior in the fluid phase with little chiral discrimination. In the solid phase the effects of chirality are much greater. Solid-fluid phase behavior involving the pure enantiomer solids and also racemic compounds was calculated. The calculations indicate that, depending on the relative sizes of the hard sphere interaction sites, packing effects alone can be sufficient to stabilize a racemic compound with respect to the pure enantiomer solids.     

计算平均力势的理论方法

A universal theoretical framework is proposed for calculating potential of mean force (PMF) between two solute particles immersed in a solvent bath, the present method overcomes all of drawbacks of previous methods. The only input required to implement the recipe is solvent density distribution profile around a single solute particle. The universal framework is applied to calculate the PMF between two large spherical particles immersed in small hard sphere solvent bath. Comparison between the present predictions and existing simulation data shows reliability of the present recipe. Effects of solvent-solute interaction detail, solvent bulk density, and solute size on the excess PMF are investigated. The resultant conclusion is that depletion of solvent component by the solute particle induces attractive excess PMF, while gathering of solvent component by the solute particle induces repulsive excess PMF, high solvent bulk density and large solute size can strengthen the tendency of attraction or repulsion. Relevance of transition from depletion attraction to gathering repulsion with the biomolecular interaction, i.e. hydrophobic attraction and hydration repulsion, is discussed.     

Origin of de-swelling and dynamics of dense ionic microgel suspensions

A direct consequence of the finite compressibility of a swollen microgel is that it can shrink and deform in response to an external perturbation. As a result, concentrated suspensions of these particles exhibit relaxation dynamics and rheological properties which can be very different with respect to those of a hard sphere suspension or an emulsion. We study the reduction in size of ionic microgels in response to increasing number of particles to show that particle shrinkage originates primarily from steric compression, and that the effect of ion-induced de-swelling of the polymer network is negligible. With increasing particle concentration, the single particle dynamics switch from those typical of a liquid to those of a super-cooled liquid and finally to those of a glass. However, the transitions occur at volume fractions much higher than those characterizing a hard sphere system. In the super-cooled state, the distribution of displacements is non-gaussian and the dependence of the structural relaxation time on volume fraction is describable by a Volger-Fulcher-Tammann function.     

Solvent density inhomogeneities and solvation free energies in supercritical diatomic fluids: a density functional approach

Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.     

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. 1. Approximate expression for the free energy of hydrophobic association based on a Gaussian-overlap model

A physics-based model is proposed to derive approximate analytical expressions for the cavity component of the free energy of hydrophobic association of spherical and spheroidal solutes in water. The model is based on the difference between the number and context of the water molecules in the hydration sphere of a hydrophobic dimer and of two isolated hydrophobic solutes. It is assumed that the water molecules touching the convex part of the molecular surface of the dimer and those in the hydration spheres of the monomers contribute equally to the free energy of solvation, and those touching the saddle part of the molecular surface of the dimer result in a more pronounced increase in free energy because of their more restricted mobility (entropy loss) and fewer favorable electrostatic interactions with other water molecules. The density of water in the hydration sphere around a single solute particle is approximated by the derivative of a Gaussian centered on the solute molecule with respect to its standard deviation. On the basis of this approximation, the number of water molecules in different parts of the hydration sphere of the dimer is expressed in terms of the first and the second mixed derivatives of the two Gaussians centered on the first and second solute molecules, respectively, with respect to the standard deviations of these Gaussians, and plausible analytical expressions for the cavity component of the hydrophobic-association energy of spherical and spheroidal solutes are introduced. As opposed to earlier hydration-shell models, our expressions reproduce the desolvation maxima in the potentials of mean force of pairs of nonpolar solutes in water, and their advantage over the models based on molecular-surface area is that they have continuous gradients in the coordinates of solute centers.     

Structures and dynamics of thermosensitive microgel suspensions studied with three-dimensional cross-correlated light scattering

The structure factors, short- and long-time diffusion coefficients, and hydrodynamic interactions of concentrated poly(N-isopropylacryamide) microgel suspensions were measured with simultaneous static and dynamic three-dimensional cross-correlated light scattering. The data are interpreted through comparison to hard sphere theory. The structure factors are known to be described well by the hard sphere approximation. When the structure factor is fit to an effective hard sphere volume fraction and radius, the diffusion and hydrodynamic interactions are also well described by the hard sphere model. We demonstrate that one single hard sphere volume fraction is sufficient to describe the microgel structures, hydrodynamic interactions, and long- and short-time collective diffusion coefficients. This result is surprising because the particle form of the microgels at these temperatures is not rigid, but rather "fuzzy" spheres with dangling polymer chains.     

Apparent molar volumes and expansibilities of 1-octanol, 1-nonanol,and 1-decanol in dilute cyclohexane solutions

The densities of solutions of 1-octanol, 1-nonanol, and 1-decanol in cyclohexane up to concentrations of 1.56 mol kg^–1 were measured at temperatures between 20 and 60°C. The apparent molar volumes and expansibilities were found to be linearly dependent on solute concentration. The excess molar volume and the excess thermal expansion coefficient of the solute were derived from the partial molar volume of the solute at infinite dilution and the solute densities. In addition, the limiting partial molar volume of the solute is discussed in terms of the scaled particle theory.     

Waterlike glass polyamorphism in a monoatomic isotropic Jagla model

We perform discrete-event molecular dynamics simulations of a system of particles interacting with a spherically-symmetric (isotropic) two-scale Jagla pair potential characterized by a hard inner core, a linear repulsion at intermediate separations, and a weak attractive interaction at larger separations. This model system has been extensively studied due to its ability to reproduce many thermodynamic, dynamic, and structural anomalies of liquid water. The model is also interesting because: (i) it is very simple, being composed of isotropically interacting particles, (ii) it exhibits polyamorphism in the liquid phase, and (iii) its slow crystallization kinetics facilitate the study of glassy states. There is interest in the degree to which the known polyamorphism in glassy water may have parallels in liquid water. Motivated by parallels between the properties of the Jagla potential and those of water in the liquid state, we study the metastable phase diagram in the glass state. Specifically, we perform the computational analog of the protocols followed in the experimental studies of glassy water. We find that the Jagla potential calculations reproduce three key experimental features of glassy water: (i) the crystal-to-high-density amorphous solid (HDA) transformation upon isothermal compression, (ii) the low-density amorphous solid (LDA)-to-HDA transformation upon isothermal compression, and (iii) the HDA-to-very-high-density amorphous solid (VHDA) transformation upon isobaric annealing at high pressure. In addition, the HDA-to-LDA transformation upon isobaric heating, observed in water experiments, can only be reproduced in the Jagla model if a free surface is introduced in the simulation box. The HDA configurations obtained in cases (i) and (ii) are structurally indistinguishable, suggesting that both processes result in the same glass. With the present parametrization, the evolution of density with pressure or temperature is remarkably similar to the corresponding experimental measurements on water. Our simulations also suggest that the Jagla potential may reproduce features of the HDA-VHDA transformations observed in glassy water upon compression and decompression. Snapshots of the system during the HDA-VHDA and HDA-LDA transformations reveal a clear segregation between LDA and HDA but not between HDA and VHDA, consistent with the possibility that LDA and HDA are separated by a first order transformation as found experimentally, whereas HDA and VHDA are not. Our results demonstrate that a system of particles with simple isotropic pair interactions, a Jagla potential with two characteristic length scales, can present polyamorphism in the glass state as well as reproducing many of the distinguishing properties of liquid water. While most isotropic pair potential models crystallize readily on simulation time scales at the low temperatures investigated here, the Jagla potential is an exception, and is therefore a promising model system for the study of glass phenomenology.     

The behavior of fluids near solutes: a density functional theory and computer simulation study

The density distribution of solvent near a solute particle is studied using density functional theory and Monte Carlo simulation. The fluid atoms interact with each other via a hard sphere plus Yukawa potential, and interact with the solute via a hard sphere potential. For small solute sizes, the solvent displays liquidlike ordering near the particle. When the solute become larger, a drying transition is observed at state points near the coexistence conditions of the solvent. These predictions are similar to those of a recent theory for the hydrophobic effect by Lum, Chandler, and Weeks [J. Phys. Chem. 103, 4570 (1999)], although a comparison with simulations shows that the theory of this work is quantitatively more accurate. The connection between density functional methods and the LCW approach is also established.     

Does confining the hard-sphere fluid between hard walls change its average properties?

We use grand canonical transition-matrix Monte Carlo and discontinuous molecular dynamics simulations to generate precise thermodynamic and kinetic data for the equilibrium hard-sphere fluid confined between smooth hard walls. These simulations show that the pronounced inhomogeneous structuring of the fluid normal to the confining walls, often the primary focus of density functional theory studies, has a negligible effect on many of its average properties over a surprisingly broad range of conditions. We present one consequence of this insensitivity to confinement: a simple analytical equation relating the average density of the confined fluid to that of the bulk fluid with equal activity. Nontrivial implications of confinement for average fluid properties do emerge in this system, but only when the fluid is both (i) dense and (ii) confined to a gap smaller than approximately three particle diameters. For this limited set of conditions, we find that "in-phase" oscillatory deviations in excess entropy and self-diffusivity (relative to the behavior of the bulk fluid at the same average density) occur as a function of gap size. These paired thermodynamic/kinetic deviations from bulk behavior appear to reflect the geometric packing frustration that arises when the confined space cannot naturally accommodate an integer number of particle layers.     

Influence of size,ellipticity and charge separation on the free energy of some aqueous bolaform electrolyte models

The free energy of some models of aqueous bolaform electrolytes have been calculated at the Debye-Hückel limiting law plus B ₂ level of approximation. The repulsive forces are modeled by hard spheres or hard ellipsoids. The charges are placed either at the center of the sphere or at the foci of the ellipsoid. Parameters were chosen to approximate the size and shape of sodium and calcium p-benzenedisufonate and sodium 4,4-biphenyldisulfonate. The results show that contrary to the standard explanations for the unusual properties of bolaform electrolytes, separating the charges has little effect on the excess free energy. It is also shown that changing from a sphere to an ellipse has little effect on the excess free energy. The most important determinates of the properties of these salts are the sizes of the ions. Agreement of the model calculations with experimental results is reasonable considering the simplicity of the models.     

定标粒子理论计算非水溶液的盐效应常数

本文应用定标粒子理论计算了非电解质溶质在盐(NaI、或KI)和环丁砜组成的非水电解质溶液中溶解度的盐效应常数。硬球作用项采用Masterton-Lee的方法。软球作用项采用胡英等的径向分布函数处理方法, 并考虑进了偶极-偶极、偶极-诱导偶极、电荷-偶极和电荷-诱导偶极等相互作用。分子的硬球直径σ和能量参数∈/k由经验方程计算。由理论值和实验结果比较得出: 当σ_2取0.563 nm、离子半径取电子密度标度时, 理论值与实验值符合得较好。     

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.     

Studies on fluids and their mixtures using the Born-Green-Yvon integral equation technique

We have developed the Born-Green-Yvon (BGY) integral equation theory for investigating the equilibrium properties of fluids and their mixtures both on the lattice and in the continuum. Using the continuum theory we have studied hard sphere fluids over a range in density having chain lengths between one and fifty sites. We have also investigated the collapse transition of a square well chain and a square well ring, each having up to four hundred sites, and have predicted the theta temperature for these systems. Turning to the case of a dilute (hard-sphere) solution we have been able to show the effect of solvation on a hard sphere chain, and captured the dependence of this effect on the ratio of hard sphere diameters of the solvent and chain segments. In all the continuum studies we have found good to excellent agreement with simulation results. We have also derived a lattice BGY theory which, while less sophisticated than the continuum version, has the advantage of producing simple closed-form expressions for thermodynamic properties of interest. This theory is capable of exhibiting the full range of miscibility behaviour observed experimentally, including upper and lower critical solution temperatures and closed-loop phase diagrams. We find that the theory does an excellent job of fitting to different kinds of experimental data and, making use of the parameters derived from fits to pure component data alone, we have been able to predict properties ranging from pure fluid vapour pressures and critical temperatures to changes in the volume and enthalpy on mixing as well as coexistence curves for solutions.     

Excess volumes of aqueous mixtures of the zwitterion and the acid chloride salt of L-amino acids

The apparent molar volumes of the zwitterion (HL) and the chloride salt form (H₂LCl) and their mixtures (HL/H₂LCl) of glycine, L-serine and L-proline have been measured in aqueous solutions at 25°C. From these experimental data the excess apparent molar volumes of the HL/H₂LCl mixtures have been calculated. An attempt is made to explain these excess volume properties in terms of intermolecular hydrogen bond formation between the solute molecules HL and H₂LCl when forming the dimer H₃L₂Cl.     

Modification of the Scaled Particle Theory for Solubility of Non-Polar Gases in Water

In this work based on the modified scaled particle theory (SPT), the solubility of non-polar gases (He, Ar, N₂, H₂, O₂, CO₂ and CH₄) in water has been studied over a wide range of temperatures. Calculations of Henry’s law constant by the SPT are related to the inherent physical properties and parameters of solvent and solute, all of which are considered temperature dependent. The temperature dependence of molar volume and hard sphere diameter of solvent and polarizability of solute have the most significant effects on the solubilities of gases in water. The average relative deviation is less than 3 %. Also, the effect of different mixing rules in the application of SPT to prediction of gas solubility has been studied.     

Charge renormalization of charged spheres based on thermodynamic properties

At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles, effective charge Z(*) is therefore invoked in the models based on Debye-Huckel approximation, such as the Derjaguin-Landau-Verwey-Overbeek potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to obtain various thermodynamic properties omega in a spherical Wigner-Seitz cell. The effect of dielectric discontinuity is examined. We show that at the same particle volume fraction, counterions around a highly charged sphere with Z may display the same value of omega as those around a weakly charged sphere with Z(*), i.e., omega(Z)=omega(Z(*)). There exists a maximally attainable value of omega at which Z=Z(*). Defining Z(*) as the effective charge, we find that the effective charge passes through a maximum and declines again due to ion-ion correlation as the number of counterions is increased. The effective charge is even smaller if one adopts the Debye-Huckel expression omega(DH). Our results suggest that charge renormalization can be performed by chemical potential, which may be observed in osmotic pressure measurements.