Various contributions to the osmotic second virial coefficient in protein-water-cosolvent solutions

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water-protein-cosolvent mixtures is developed. The Kirkwood-Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water-protein-cosolvent mixtures. These properties can be divided into two groups: (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water-cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions: (1) one due to the protein-solvent interactions B2(p-s), which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B2(p-p)), and (3) a third one representing an ideal mixture contribution (B2(id)). The cosolvent composition dependencies of these three contributions were examined for several water-protein-cosolvent mixtures using experimental data regarding the OSVC and the preferential binding parameter. For the water-lysozyme-arginine mixture, it was found that OSVC exhibits the behavior of an ideal mixture and that B2(id) provides the main contribution to the OSVC. For the other mixtures considered (water-Hm MalDH-NaCl, water-Hm MalDH-(NH4)2SO4, and water-lysozyme-NaCl mixtures), it was found that the contribution of the protein-solvent interactions B2(p-s) is responsible for the composition dependence of the OSVC on the cosolvent concentration, whereas the two remaining contributions (B2(p-p)) and B2(id)) are almost composition independent.     

Local composition in the vicinity of a protein molecule in an aqueous mixed solvent

This paper is focused on the composition of a cosolvent in the vicinity of a protein surface (local composition) and its dependence on various factors. First, the Kirkwood-Buff theory of solution is used to obtain analytical expressions that connect the excess or deficit number of cosolvent and water molecules in the vicinity of a protein surface with experimentally measurable quantities such as the bulk concentration of the mixed solvent, the preferential binding parameter, and the molar volumes of water and cosolvent. Using these expressions, relations between the preferential binding parameter (at a molal concentration scale) and the above excesses (or deficits) are established. In addition, the obtained expressions are used to examine the effect of the nonideality of the water + cosolvent mixtures and of the molar volume of the cosolvent on the excess (or deficit) number of cosolvent molecules in the vicinity of the protein surface. It is shown that at least for the mixed solvents considered (water + urea and water + glucose) the nonideality of the mixed solvent is not an important factor in the local compositions around a protein molecule and that the main contribution is provided by the nonidealities of the protein-water and protein-cosolvent mixtures. Special attention is paid to urea as cosolvent, because urea is one of only a few compounds with a concentration at the protein surface larger than its concentration in the bulk. The composition dependence of the excess of urea around a protein molecule is calculated for the water + lysozyme + urea mixture at pH = 7.0 and 2.0. At pH = 7.0, the excess of urea becomes almost composition independent at high urea concentrations. Such independence could be explained by assuming that urea totally replaces water in some areas of the protein surface, whereas on the remaining areas of the protein surface both water and urea are present with concentration comparable to those in the bulk. The Schellman exchange model was used to relate the preferential binding parameter in water + lysozyme + urea mixtures to the urea concentration.     

The Kirkwood-Buff theory and the effect of cosolvents on biochemical reactions

Cosolvents added to aqueous solutions of biomolecules profoundly affect protein stability, as well as biochemical equilibria. Some cosolvents, such as urea and guanidine hydrochloride, denature proteins, whereas others, such as osmolytes and crowders, stabilize the native structures of proteins. The way cosolvents interact with biomolecules is crucial information required to understand the cosolvent effect at a molecular level. We present a statistical mechanical framework based upon Kirkwood-Buff theory, which enables one to extract this picture from experimental data. The combination of two experimental results, namely, the cosolvent-induced equilibrium shift and the partial molar volume change upon the reaction, supplimented by the structural change, is shown to yield the number of water and cosolvent molecules bound or released during a reaction. Previously, denaturation experiments (e.g., m-value analysis) were analyzed by empirical and stoichiometric solvent-binding models, while the effects of osmolytes and crowders were analyzed by the approximate molecular crowding approach for low cosolvent concentration. Here we synthesize these previous approaches in a rigorous statistical mechanical treatment, which is applicable at any cosolvent concentration. The usefulness and accuracy of previous approaches was also evaluated.     

Densities and volume properties of (water + tert-butanol) over the temperature range of (274.15 to 348.15) K at pressure of 0.1 MPa

The densities of {water (1) + tert-butanol (2)} binary mixture were measured over the temperature range (274.15 to 348.15) K at atmospheric pressure using “Anton Paar” digital vibrating-tube densimeter. Density measurements were carried out over the whole concentration range at (308.15 to 348.15) K. The following volume parameters were calculated: excess molar volumes and thermal isobaric expansivities of the mixture, partial molar volumes and partial molar thermal isobaric expansivities of the components. Concentration dependences of excess molar volumes were fitted with Redlich–Kister equation. The results of partial molar volume calculations using four equations were compared. It was established that for low alcohol concentrations at T ? 208 K the inflection points at x₂ ≈ 0.02 were observed at concentration dependences of specific volume. The concentration dependences of partial molar volumes of both water and tert-butanol had extremes at low alcohol content. The temperature dependence of partial molar volumes of water had some inversion at х₂ ≈ 0.65. The temperature dependence of partial molar volumes of tert-butanol at infinite dilution had minimum at ≈288 K. It was discovered that concentration dependences of thermal isobaric expansivities of the mixture at small alcohol content and low temperatures passed through minimum.     

Chiral recognition between a substituted cyclooctatetraene dianion and a half crown ether substituted with ibuprofen

(S)-Verbenol was substituted onto cyclooctatetraene (COT) via an ether linkage. In tetrahydrofuran (THF), Cs(+) or Na(+) counterions are tightly ion associated with the verbenoxy-COT dianion. A cosolvent, consisting of an ibuprofen unit connected to a half crown ether, was added to the verbenoxy-COT(2)(-),M(+)(2) solutions. The intimate interaction between the chiral cosolvent (ibuprofoxymethoxyethoxyethane) and the ion-associated counterion (either Na(+) or Cs(+)) forces a chiral recognition between the verbenoxy moiety and the ibuprofoxy moiety. When a molar excess of the cosolvent is present in the dianion THF solution, separation of the cosolvent associated with the verbenoxy-COT(2)(-),M(+)(2) complex from the uncomplexed cosolvent allows partial resolution of the enantiomers of ibuprofoxymethoxyethoxyethane.     

Hydration of alcohol clusters in 1-propanol-water mixture studied by quasielastic neutron scattering and an interpretation of anomalous excess partial molar volume

Quasielastic neutron scattering measurements have been made for 1-propanol-water mixtures in a range of alcohol concentration from 0.0 to 0.167 in mole fraction at 25 degrees C. Fraction alpha of water molecules hydrated to fractal surface of alcohol clusters in 1-propanol-water mixture was obtained as a function of alcohol concentration. Average hydration number N(ws) of 1-propanol molecule is derived from the value of alpha as a function of alcohol concentration. By extrapolating N(ws) to infinite dilution, we obtain values of 12-13 as hydration number of isolated 1-propanol molecule. A simple interpretation of structural origin of anomalous excess partial molar volume of water is proposed and as a result a simple equation for the excess partial molar volume is deduced in terms of alpha. Calculated values of the excess partial molar volumes of water and 1-propanol and the excess molar volume of the mixture are in good agreement with experimental values.     

Pressure perturbation calorimetric studies of the solvation properties and the thermal unfolding of proteins in solution--experiments and theoretical interpretation

We used pressure perturbation calorimetry (PPC), a relatively new and efficient technique, to study the solvation and volumetric properties of amino acids and peptides as well as of proteins in their native and unfolded state. In PPC, the coefficient of thermal expansion of the partial volume of the protein is deduced from the heat consumed or produced after small isothermal pressure jumps, which strongly depends on the interaction of the protein with the solvent or cosolvent at the protein-solvent interface. Furthermore, the effects of various chaotropic and kosmotropic cosolvents on the volume and expansivity changes of proteins were measured over a wide concentration range with high precision. Depending on the type of cosolvent and its concentration, specific differences were found for the solvation properties and unfolding behaviour of the proteins, and the volume change upon unfolding may even change sign. To yield a molecular interpretation of the different terms contributing to the partial protein volume and its temperature dependence, and hence a better understanding of the PPC data, molecular dynamics computer simulations on SNase were also carried out and compared with the experimental data. The PPC studies introduced aim to obtain more insight into the basic thermodynamic properties of protein solvation and volume effects accompanying structural transformations of proteins in various cosolvents on one hand, as these form the basis for understanding their physiological functions and their use in drug designing and formulations, but also to initiate further valuable applications in studies of other biomolecular and chemical systems.     

Volumetric properties of aqueous electrolytes at high temperature. III. B(OH)3−NaBx(OH)3x+1−NaOH mixtures up to 523 K

The densities of aqueous solutions resulting from the partial neutralization of boric acid with sodium hydroxide were measured as a function of concentration, between 375 K and 523 K at pressures close to saturation. The speciation in this system is complex, di- and triborate ions are present in addition to the monoborate ion. The concentration dependence of the apparent partial molar volume of the mixture can be described using the Pitzer equation only if the formation of the polyborate species in the concentrated solutions is taken into account. The partial molar volumes at infinite dilution for the diborate and triborate anions, obtained by assuming ideal mixing, are reported in the range of temperature studied.     

Volumetric properties of the (tetrahydrofuran + water) and (tetra-n-butyl ammonium bromide + water) systems: Experimental measurements and correlations

In this communication, we report experimental density data for the binary mixtures of (water + tetrahydrofuran) and (water + tetra-n-butyl ammonium bromide) at atmospheric pressure and various temperatures. The densities were measured using an Anton Paar™ digital vibrating-tube densimeter. For the (tetrahydrofuran + water) system, excess molar volumes have been calculated using the experimental densities and correlated using the Redlich–Kister equation. The Redlich–Kister equation parameters have been adjusted on experimental results. The partial molar volumes and partial excess molar volumes at infinite dilution have also been calculated for each component. A simple density equation was finally applied to correlate the measured density of the (tetra-n-butyl ammonium bromide + water) system.     

Theoretical study of the cosolvent effect on the partial molar volume change of staphylococcal nuclease associated with pressure denaturation

We explain the molecular mechanism of the effect of urea and glycerol cosolvents on the partial molar volume (PMV) change associated with the pressure denaturation of staphylococcal nuclease (SNase) protein recently observed in experiments. Native and denatured conformations of SNase are produced by using molecular dynamics simulations in water, and the PMV is obtained from the integral equation theory of molecular liquids called 3D-RISM, which is based on statistical mechanics. The PMV of the native SNase in water predicted by 3D-RISM theory is in good agreement with experiment. The PMV changes associated with pressure denaturation in water and in water-urea and water-glycerol mixtures are qualitatively reproduced. By analyzing the results obtained, we found two interesting cosolvent effects on the PMV: (1) both urea and glycerol cosolvents increase the PMVs of both native and denatured SNase compared to those in water and (2) both urea and glycerol cosolvents increase the PMV of denatured SNase more than that of native SNase. We also showed that these two observations can be explained in terms of the thermal volume, which is related to the packing effect of solvent molecules.     

Volumetric behavior of a bolaamphiphile in different amides-water and ethylene glycol-water mixtures

The effect of binary aqueous mixtures of ethylene glycol (EG), formamide (FA), N-methylformamide (NMF), dimethylformamide (DMF), and their pure phase on the apparent molar volume phi(V) of the bolaamphiphile decamethonium bromide (C10Me6) has been investigated at 298.15 K. The behavior of standard molar volumes V2(0) and transfer volumes Delta(t)phi(V) of C10Me6 from water to solvent/water (S/W) binary mixtures, shows different minima and maxima depending on the composition of the solvent. This behavior is influenced by the nature of the cosolvent and on the type of the solute and more or less corresponds to volumetric changes in the S/W mixture. The investigation of the transfer volumes in different fixed concentrations reveals an inversion of Delta(t)phi(V) values between the compositions, which suggests a differentiation of the effects of different volume contributions on the partial molar volume of ions. The correlation of Delta(t)phi(V) with the dielectric constant of the aqueous amide mixtures shows that the behavior of Delta(t)phi(V) vs x(amide) reflects the changes of epsilon(E) vs x(amide).     

L-苏氨酸在糖及维生素C水溶液中的体积性质

用精密数字密度计和粘度计测定了L-苏氨酸在不同质量分数的葡萄糖、蔗糖及维生素C水溶液中的密度和粘度，计算了L-苏氨酸的极限偏摩尔体积、迁移偏摩尔体积、理论水化数和粘度B系数，讨论了溶剂组成变化对L-苏氨酸迁移偏摩尔体积、粘度B系数和理论水化数的影响.结果表明，随混合溶剂中共溶质含量的增加，迁移偏摩尔体积、粘度B系数随之增加；而由于葡萄糖、蔗糖及维生素C分子与L-苏氨酸荷电中心的直接相互作用，削弱了两性离子带电中心对周围水分子的电致收缩效应，造成了理论水化数随其含量的增加而减小.     

Volumetric Properties of Binary Mixtures of Glycerol + <Emphasis Type="Italic">tert</Emphasis>-Butanol over the Temperature Range 293.15 to 348.15 K at Atmospheric Pressure

Densities of glycerol (1) + tert-butanol (2) mixtures were measured over the temperature range 293.15 to 348.15 K at atmospheric pressure, over the entire composition range, with a vibrating tube densimeter. Excess molar volumes, apparent and partial molar volumes of glycerol and tert-butanol, thermal isobaric expansivities of the mixture and partial molar expansivities of the components were calculated. The excess molar volumes of the mixtures are negative at all temperatures, and deviations from ideality increase with increasing temperature. Excess molar volumes were fitted to the Redlich–Kister equation. Partial molar volumes of glycerol decrease with increasing tert-butanol concentration. The temperature dependence of the partial molar volumes of glycerol is characterized by an inversion at x ₂≈0.7. “Negative expansion” of the limiting partial volumes of glycerol was observed.     

Density,partial molar volume,and excess volume of solutions of acrylic acid in acetonitrile, 1,2-dichloroethane,hexane, and benzene at 293 K

Using pycnometric method, we have measured density of the solutions of acrylic acid in acetonitrile, 1,2-dichloroethane, hexane, and benzene at 293 K and atmospheric pressure. The values of the excess molar volume for these systems and the values of the partial molar volumes of components were derived. In the whole concentration range the excess molar volume for binary mixtures of acrylic acid and either 1,2-dichloroethane, or benzene, or hexane has positive values, and in the system of acrylic acid-acetonitrile the value is negative.     

Changes in partial molar volume and isentropic partial molar compressibility of self-association of purine and caffeine in aqueous solution at 1–1600 bar

Ultrasound measurements of purine and caffeine in aqueous solution as function of pressure are reported at 25°C and used to calculate the changes in their partial molar volumes and partial molar compressibilities due to self-association. The effect of pressure is to increase the association. The volume changes are negative for the self-association process, becoming less negative with increasing pressure. This is caused by the monomer in the associated state. The partial molar volume of the monomer in the associated state increases with pressure, contrary to what is expected for nonelectrolytes in water. Hydration of the associated monomer must be a key to this increase. The result suggest that dipole-induced dipole interactions is a possible mechanism for the association process and not hydrophobic interactions. The change in the partial molar compressibility of the association is positive, decreasing with increasing pressure.     

Molar excess volumes of 1,4-dioxane+ acetonitrile,n-butylamine+acetonitrile andn-butylamine+1,4-dioxane at different temperatures

Molar excess volumes and partial molar volumes are reported for binary mixtures of 1,4-dioxane + acetonitrile, n-butylamine + acetonitrile and n-butylamine + 1,4-dioxane at five different temperatures and over the complete concentration range. The Prigogine-Flory-Patterson model of solution thermodynamics has been used to predict the excess molar volumes. This work shows the importance of the three contributions: interactional, internal pressure and free volume, to the excess volume.     

Densities and Apparent Molar Volumes of Aqueous NaNO3 Solutions at Temperatures from 292 to 573 K and at Pressures Up to 30 MPa

Densities of four aqueous NaNO₃ solutions (0.100, 0.303, 0.580, 0.892 mol-kg^–1 H₂O) have been measured in the liquid phase with a constant-volume piezometer immersed in a precision liquid thermostat. Measurements were made at ten isotherms between 292 and 573 K. The range of pressure was 0.1–30 MPa. The total uncertainty of density, pressure, temperature, and concentration measurements were estimated to be less than 0.06%, 0.05%, 10 mK, and 0.014%, respectively. Values of saturated densities were determined by extrapolating experimental P- data to the vapor pressure at fixed temperature and composition. Apparent molar volumes were derived using measured values of density for the solutions and for pure water. The apparent molar volumes were extrapolated to zero concentration to yield partial molar volumes at infinite dilution. The temperature, pressure, and concentration dependence of partial and apparent molar volumes were studied. The measured values of density and apparent and partial molar volume were compared with data reported in the literature.     

288.15, 298.15和308.15 K温度条件下甘氨酰甘氨酸在蔗糖-水混合溶剂中的体积性质研究

利用Anton Paar DMA55精密数字密度计测定了288.15, 298.15和308.15 K甘氨酰甘氨酸在蔗糖-水混合溶剂中的密度, 计算了甘氨酰甘氨酸的表观摩尔体积VΦ和极限偏摩尔体积 , 得到了其由纯水溶剂转移至混合溶剂中的迁移偏摩尔体积Δtrs 和理论水化数Nh．根据共球交盖模型, 讨论了迁移偏摩尔体积和水化数的变化规律．结果表明, 甘氨酰甘氨酸带电中心与蔗糖之间的结构相互作用对其迁移体积有正贡献, 且占主导地位．甘氨酰甘氨酸的迁移偏摩尔体积为正值, 且随着蔗糖浓度的增大而增大; 理论水化数随温度升高、蔗糖浓度的增大而减小; 温度升高, 极限偏摩尔体积增大, 迁移偏摩尔体积变化很小．     

Bulk properties of a liquid phase mixture {ethylene glycol+<Emphasis Type="Italic">tert</Emphasis>-butanol} in the temperature range 278.15–348.15 K and pressures of 0.1-100 MPa. I. Experimental results,excess and partial molar volumes

The densities ρ and coefficients of compressibility k = ΔV/V ₀ of a binary mixture {ethylene glycol (1) + tert-butanol (2)} in the temperature range of 278.15–323.15 K and pressures of 0.1–100 MPa over the entire range of compositions of liquid phase state are measured. Found that the coefficients of compressibility k of the mixture increase both with an increase in the concentration of tert-butanol and with a rise in temperature and pressure. The excess molar volumes of the mixture, apparent, partial molar volumes, and limiting partial molar volumes of the components are calculated. It is showed that the excess molar volumes of the mixture are negative and decrease when the pressure increases. The excess molar volumes are described by the Redlich-Kister equation. The partial molar volumes of ethylene glycol sharply decrease in the range of high concentrations of tert-butanol. The dependences of partial molar volumes of ethylene glycol are characterized by the presence of a region of temperature inversion. The “negative compressibility” of the limiting partial volumes of ethylene glycol is revealed.     

Molar volumes of aqueous and ethylene glycol solutions of tetrahydrofuran

The densities of ethylene glycol solutions of tetrahydrofuran (THF) with 0–20 mol % THF were measured at 20–60°C and atmospheric pressure to an accuracy of 5 × 10⁻⁵ g/cm³. The apparent molar volumes of THF in the solutions were calculated and their concentration and temperature dependences determined. The results were compared with the apparent molar volumes of THF in aqueous systems calculated from the literature data. Minima were found on the concentration dependence of the apparent volume of THF for both aqueous and ethylene glycol solutions and changed differently as the temperature increased. The data obtained were discussed from the standpoint of solvophobic effects in aqueous and ethylene glycol solutions of THF.