Partial Molar Isothermal Compressions Research Articles

Kirkwood-Buff integration: A promising route to entropic properties?

Kirkwood-Buff integration (KBI) is implemented into the massively-parallel molecular simulation tool ms2 and assessed by molecular dynamics simulations of binary liquid mixtures. The formalism of Krüger et al. (P. Krüger et al., J. Phys. Chem. Lett. 4: 235–238, 2013) that adopts NVT ensemble data to the μVT ensemble is employed throughout. Taking advantage of its linear scaling with inverse system size, the extrapolation to the thermodynamic limit is analyzed. KBI are calculated with standard radial distribution functions (RDF) and two corrected RDF forms. Simulations in the NVT ensemble are carried out in the entire composition range for four Lennard-Jones mixtures, studying system size dependence by varying N = 4000, 8000 and 16000 molecules. Moreover, four mixtures of “real” components are considered with N = 4000. Thermodynamic factor, partial molar volumes and isothermal compressibility are calculated from KBI and compared with benchmark data from NpT ensemble simulations. The assessment shows that the formalism of Krüger et al. greatly improves KBI and that extrapolation is important, particularly for smaller systems.

Density and volumetric properties of the aqueous solutions of urea at temperatures from T = (278 to 333) K and pressures up to 100 MPa

Abstract This paper highlights the values of densities of aqueous solutions of urea in the concentration range m (from 0.1809 to 12.801) mol·kg−1 at T = (278.15, 288.15, 298.15, 308.15, 323.15 and 333.15) K and at p = (0.101, 10, 25, 50, 75 and 100) MPa. The densities were also measured for dilute aqueous solutions m (from 0.093 to 2.505) mol·kg−1 with temperature from 274.15 to 283.15 K, with increment of 1 K at atmospheric pressure, in order to study the effect of urea on the temperature of the maximum water density. Volumetric properties calculated from the density, such as apparent molar volumes of urea, Vɸ,2, molar isothermal compressions, KT,m, and molar isobaric thermal expansions, EP,m, of solution are considered depending on concentration, temperature and pressure. Also, certain volumetric characteristics for infinitely diluted urea in water were obtained: the limiting partial molar volumes, V 2 ∞ ; limiting partial molar isothermal compressions, K T , 2 ∞ ; and limiting partial molar isobaric thermal expansions, E P , 2 ∞ . Obtained results are discussed from the standpoint of solute – solute and solute – solvent interactions. With the help of various approaches based on volumetric characteristics, the character of the disturbing effect of urea on the water structure was described.

High-pressure densities and derived properties of binary {methyl tert-butyl ether (MTBE) + alcohols} mixtures

In this study, density of binary liquid mixtures of {methyl tert-butyl ether (MTBE) + ethanol, or + 1-propanol, or + 1-butanol} has been determined as a function of composition at temperature 290 K and pressure up to 35 MPa. Densities data were measured using an Anton Paar DMA 4500 vibrating tube densimeter coupled to an external Anton Paar DMA HP high-pressure cell. A Tait equation was used to correlate experimental densities with pressure. The experimental results have been used to calculate the derived volumetric properties such as excess molar volumes ( $$V_{\text{m}}^{\text{E}}$$ ), apparent molar volumes ( $$V_{{\upphi{\text{i}}}}$$ ), partial molar volume ( $$\bar{V}_{\text{i}}$$ ) and isothermal compressibility (κ T). The thermodynamic results suggest that the structural effects and intermolecular interactions must outweigh other possible effects present in the mixtures studied.

Densities and Volumetric Properties of Aqueous Solutions of {Water (1) + N-Methylurea (2)} Mixtures at Temperatures of 274.15–333.15 K and at Pressures up to 100 MPa

Densities of the mixture {water (1) + N- methylurea (2)} in the concentration range to mole fraction x2 = 0.07071 (or to the solution molality concentration m2 = 4.22335 mol·kg–1) at atmospheric pressure in the temperature range from 274.15 to 333.15 K and compression k = ΔV/V0 at pressures to 100 MPa (10, 25, 50, 75, and 100) in the temperature range from 278.15 to 323.15 K (278.15, 288.15, 288.15, 308.15, 323.15) in the same concentration range were calculated in this study. The apparent molar volumes of N-methylurea Vϕ,2 and the partial molar volumes of both components V̅1 and V̅2 in the mixture, molar isothermal compressibilities KT,m, molar isobaric thermal expansions EP,m, and isochoric coefficients of thermal pressure β of the mixture were calculated. Moreover, volumetric measures for the infinitely dilute solution of N-methylurea solution were calculated: limiting partial molar volumes V̅2∞, the limiting partial molar isothermal compressibilities K̅T,2∞, and the limiting partial molar isobaric thermal expansions E̅P,2∞. The results obtained are discussed from the point of view of solute–solvent and solute–solute interactions.

The Partial Molar Isothermal Compressions of the Nucleosides Adenosine, Cytidine, and Uridine in Aqueous Solution at T = (288.15 and 313.15) K

Sound speeds have been measured for aqueous solutions of the nucleosides adenosine, cytidine, and uridine at T = (288.15 and 313.15) K and at ambient pressure. The partial molar isentropic compressions at infinite dilution, \( K_{S,2}^{\text{o}} \), were derived from the speed of sound data. The partial molar heat capacities at infinite dilution, \( C_{p,2}^{\text{o}} \), for the three nucleosides at T = (288.15 and 313.15) K were also determined. These \( K_{S,2}^{\text{o}} \) and \( C_{p,2}^{\text{o}} \) results, along with partial molar isobaric expansions at infinite dilution, \( E_{2}^{\text{o}} = \, (\partial V_{2}^{\text{o}} /\partial T)_{p} \), that were derived using data from the literature, were used to evaluate the partial molar isothermal compressions at infinite dilution, \( K_{T,2}^{\text{o}} \{ K_{T,2}^{\text{o}} = - \, (\partial V_{2}^{\text{o}} /\partial p)_{T} \} \), for the nucleosides. The \( K_{T,2}^{\text{o}} \) results were rationalized in terms of nucleoside hydration and its temperature dependence.

Thermodynamic properties of peptide solutions 20. Partial molar volumes and isothermal compressions for some tripeptides of sequence gly-X-gly (X = gly, ala, leu, asn, thr, and tyr) in aqueous solution at T = 298.15 K and p = (10–120) MPa

Sound speeds have been measured for aqueous solutions of six tripeptides of sequence glycyl-X-glycine, where X is one of the amino acids glycine, alanine, leucine, asparagine, threonine, and tyrosine at T=298.15K and at the pressures p=(10, 20, 40, 60, 80, 100, and 120)MPa. Using methods described in previous work, these sound speeds were used to derive the partial molar volumes at infinite dilution, V2o, the partial molar isentropic compressions at infinite dilution, KS,2o, and the partial molar isothermal compressions at infinite dilution, KoT,2 {KoT,2=−(∂V2o/∂p)T}, for the tripeptides in aqueous solution at the elevated pressures. The results were used to calculate the partial molar volumes and partial molar isothermal compressions for the various amino acid side-chains over the pressure range p=(10–120)MPa.

The Energetics of a Three‐State Protein Folding System Probed by High‐Pressure Relaxation Dispersion NMR Spectroscopy

AbstractThe energetic and volumetric properties of a three‐state protein folding system, comprising a metastable triple mutant of the Fyn SH3 domain, have been investigated using pressure‐dependent 15N‐relaxation dispersion NMR from 1 to 2500 bar. Changes in partial molar volumes (ΔV) and isothermal compressibilities (ΔκT) between all the states along the folding pathway have been determined to reasonable accuracy. The partial volume and isothermal compressibility of the folded state are 100 mL mol−1 and 40 μL mol−1 bar−1, respectively, higher than those of the unfolded ensemble. Of particular interest are the findings related to the energetic and volumetric properties of the on‐pathway folding intermediate. While the latter is energetically close to the unfolded state, its volumetric properties are similar to those of the folded protein. The compressibility of the intermediate is larger than that of the folded state reflecting the less rigid nature of the former relative to the latter.

The energetics of a three-state protein folding system probed by high-pressure relaxation dispersion NMR spectroscopy.

The energetic and volumetric properties of a three-state protein folding system, comprising a metastable triple mutant of the Fyn SH3 domain, have been investigated using pressure-dependent (15) N-relaxation dispersion NMR from 1 to 2500 bar. Changes in partial molar volumes (ΔV) and isothermal compressibilities (ΔκT ) between all the states along the folding pathway have been determined to reasonable accuracy. The partial volume and isothermal compressibility of the folded state are 100 mL mol(-1) and 40 μL mol(-1) bar(-1) , respectively, higher than those of the unfolded ensemble. Of particular interest are the findings related to the energetic and volumetric properties of the on-pathway folding intermediate. While the latter is energetically close to the unfolded state, its volumetric properties are similar to those of the folded protein. The compressibility of the intermediate is larger than that of the folded state reflecting the less rigid nature of the former relative to the latter.

Volumetric Properties at High Pressures of the Nucleosides Inosine, 2′-Deoxyinosine, and 2′-Deoxyguanosine and the Volumetric Properties of Guanosine Derived Using Group Additivity Methods

Sound speeds have been measured for aqueous solutions of the nucleosides inosine, 2′-deoxyinosine, and 2′-deoxyguanosine at T = 298.15 K and at the pressures p = (0.1, 10, 20, 40, 60, 80, and 100) MPa. Using methods described in previous work, these sound speeds were used to derive the partial molar volumes at infinite dilution, V2o, the partial molar isentropic compressions at infinite dilution, KS,2o, and the partial molar isothermal compressions at infinite dilution, KT,2o {KT,2o = −(∂V2o/∂p)T}, for the nucleosides in aqueous solution at the elevated pressures. A semiempirical model was used to rationalize the KT,2o results in terms of changes in hydration of the solutes as a function of pressure. Group additivity methods were used to derive values of V2o and KT,2o over the pressure range p = (10 to 100) MPa for the sparingly soluble nucleoside guanosine.

Characterization of the volumetric properties of betaine in aqueous solutions: Compositional, pressure, and temperature dependence

Densities, ρ, at atmospheric pressure and coefficients of compressibility, k, at p = (10, 25, 50, 75, 100) MPa were measured for aqueous solutions of N,N,N-trimethylglycine (betaine) at T = (278.15, 288.15, 298.15, 308.15 323.15) K. The experimental data have been used to calculate the following volumetric parameters: the apparent molar volume of betaine, Vϕ,2, the molar isothermal compression, KT,m, and the molar isobaric expansion, EP,m, of solutions at all pressures and temperatures studied. Some parameters for infinite dilute solution of betaine in water were also obtained such as limiting partial molar volumes, V2∞, limiting partial molar isothermal compressions, KT,2∞, and limiting partial molar isobaric expansions, EP,2∞. The variation of all these parameters with composition, temperature, and pressure were discussed from the viewpoint of intermolecular interactions in the system.

The density and compressibility of CaO–FeO–SiO2 liquids at one bar: Evidence for four-coordinated Fe2+ in the CaFeO2 component

Double-bob density measurements using molybdenum bobs in a reducing atmosphere were made on hedenbergite (CaFeSi2O6) liquid and four other CaO–FeO–SiO2 (CFS) liquids that each contains 40mol% FeO and variable CaO and SiO2 concentrations. In addition, relaxed sound speeds were measured with an acoustic interferometer at centered frequencies of 4.5 and 5.5MHz between 1571 and 1885K. An ideal mixing model using the oxide components (CaO–FeO–SiO2) for molar volume and isothermal compressibility cannot recover the experimental results within error. When each experimental liquid is fitted individually, the partial molar volume and isothermal compressibility of the FeO component (V¯T,FeO and β¯T,FeO, respectively) increase systematically with CaO concentration, consistent with a composition-induced decrease in the average Fe2+ coordination number. When the four CFS liquids with 40mol% FeO are recast in terms of the CaFeO2–FeO–SiO2 components, an ideal mixing model for both volume and compressibility recovers the data for the four liquids within experimental error. At 1723K, the fitted V¯FeO and β¯FeO values (±1σ) are 12.1 (±0.2)cm3/mol and 3.5 (±0.3)×10−2GPa−1, respectively, which are postulated to reflect 6-coordinated Fe2+ given the similarity of V¯FeO in the melt to the molar volume of crystalline FeO (wüstite). In contrast, the derived values of V¯FeO and β¯FeO from the CaFeO2 component are 17.1 (±0.2)cm3/mol and 7.1 (±0.2)×10−2GPa−1, respectively, which are postulated to reflect Fe2+ in 4-fold given that crystalline CaFeO2 contains 4-coordinated Fe2+. These two end-member values for V¯FeO at 1723K are used to develop a linear equation to calculate Fe2+ coordination as a function of V¯FeO, which leads to average Fe2+ coordination numbers in the CFS liquids that range from 5.2 to 4.6, including a value of 4.6 (±0.2) for hedenbergite (CaFe2Si2O6) liquid. The key to developing a model equation for density and compressibility for FeO-bearing magmatic liquids is to determine how melt composition affects Fe2+ coordination.

Liquid phase PVTx properties of binary mixtures of (water + ethylene glycol) in the range from 278.15 to 323.15 K and from 0.1 to 100 MPa. II. Molar isothermal compressions, molar isobaric expansions, thermal pressure coefficients and internal pressure

Molar isothermal compressions, molar isobaric expansions, molar coefficients of thermal pressure, and internal pressures of {water (1)+ethylene glycol (2)} mixture over the whole concentration range, as well as partial molar isothermal compressions and partial isobaric expansions of water in ethylene glycol and of ethylene glycol in water at infinite dilution were calculated at pressures from 0.1 to 100MPa and at temperatures from 278.15 to 323.15K. It was revealed that concentration dependences of molar isothermal compressions KT,m, molar isobaric expansions EP,m, and thermal pressure coefficients, β, on ethylene glycol molar fraction had extremes. Temperature and baric dependences of internal pressure of the mixture were almost linear, and coefficients of these dependences at low ethylene glycol concentrations differed from those coefficients for water, ethylene glycol, and their mixtures with high diol content. Analysis of the volume characteristics obtained confirmed both hydrophilic and hydrophobic ethylene glycol nature.

Volumetric properties of the nucleosides adenosine, cytidine, and uridine in aqueous solution at T = 298.15 K and p = (10 to 120) MPa

Sound speeds have been measured for aqueous solutions of the nucleosides adenosine, cytidine, and uridine at T=298.15K and at the pressures p=(10, 20, 40, 60, 80, 100, and 120)MPa. Using methods described in previous work, these sound speeds were used to derive the partial molar volumes at infinite dilution, V2o, the partial molar isentropic compressions at infinite dilution, KS,2o, and the partial molar isothermal compressions at infinite dilution, KT,2o{KT,2o=-(∂V2o/∂p)T}, for the nucleosides in aqueous solution at elevated pressures. The V2o and KT,2o results were rationalized in terms of the likely solute–water interactions. The V2o results were also critically compared with those calculated using the revised Helgeson–Kirkham–Flowers (HKF) equation of state.

Protein Conformational Intermediates Characterized with Novel High Pressure EPR and CD Techniques

Regulation of protein function is often linked to conformational intermediates that exist in equilibrium with the ground state. In many cases, these intermediate states exist as only a small fraction of the total protein conformational ensemble. It has been shown that high hydrostatic pressure is an invaluable tool for populating low-lying, excited states to levels amenable to spectroscopic detection. Here we demonstrate the usefulness of high pressure for populating such states as monitored by two novel techniques: High pressure electron paramagnetic resonance spectroscopy (EPR) and high pressure circular dichroism (CD). High pressure EPR was used in conjunction with site-directed spin labeling to monitor changes in local protein structure with applied pressure (up to 400 MPa). The relative partial molar volume and isothermal compressibility of each conformational substate was determined from the pressure dependence of the equilibrium constant determined from the continuous wave EPR spectra. High pressure CD was employed to detect global changes in secondary and tertiary structure at elevated pressure (up to 200 MPa). The combination of site-specific and global information provided by these techniques provides a more complete description of pressure excited intermediate states. Data from apomyoglobin and a cavity containing mutant (L99A) of T4 lysozyme are presented.

Amorphous Materials: Properties, Structure, and Durability: Compositional dependent compressibility of dissolved water in silicate glasses

The sound velocities and elastic properties of a series of hydrous rhyolite, andesite, and basalt glasses have been determined by Brillouin scattering spectroscopy at ambient conditions to elucidate the effect of glass composition on the compressibility of dissolved water. Both the adiabatic bulk (K S ) and shear modulus (μ) of the dry glasses decrease with increasing silica content (K S,basalt > K S,andesite > K S,rhyolite and μ basalt > μ andesite > μ rhyolite ). For each composition, the shear modulus systematically decreases with increasing water content. Although the addition of up to 14 mol% water decreases the K S of andesite and basalt glasses by up to 6%, there is no discernable effect of water on the K S of the rhyolite glasses. The partial molar KS of dissolved water (K S ) in rhyolite, andesite, and basalt glasses are 37 ± 5, 19 ± 7, and 40 ± 3 GPa, corresponding to partial molar isothermal compressibilities (β̅ T ) of 0.029 ± 0.005, 0.042 ± 0.004, and 0.026 ± 0.002 GPa −1 , respectively. These results indicate that the compressibility of dissolved water strongly depends on the bulk composition of the glass; hence, the partial molar volume of water cannot be independent of the bulk composition at elevated pressure. If the compressibility of dissolved water also depends on composition in the analog melts at high temperature and pressure, these observations will have important consequences for magmatic processes such as magma mixing/unmixing and fractional crystallization.

The partial molar heat capacity, expansion, isentropic, and isothermal compressions of thymidine in aqueous solution at T = 298.15 K

Solution densities have been determined for aqueous solutions of thymidine at T = (288.15, 298.15, 303.15, and 313.15) K. The partial molar volumes at infinite dilution, V 2 ∘ , obtained from the density data were used to derive the partial molar isobaric expansion at infinite dilution for thymidine at T = 298.15 K, E 2 ∘ { E 2 ∘ = ( ∂ V 2 ∘ / ∂ T ) p } . The partial molar heat capacity at infinite dilution for thymidine, C p , 2 ∘ , at T = 298.15 K has also been determined. Sound speeds have been measured for aqueous solutions of thymidine at T = 298.15 K. The partial molar isentropic compression at infinite dilution, K S , 2 ∘ , and the partial molar isothermal compression at infinite dilution, K T , 2 ∘ { K T , 2 ∘ = - ( ∂ V 2 ∘ / ∂ P ) T } , have been derived from the sound speed data. The V 2 ∘ , E 2 ∘ , C p , 2 ∘ , and K S , 2 ∘ results for thymidine are critically compared with those available from the literature.

Fluctuation theory of molecular association and conformational equilibria

General expressions relating the effects of pressure, temperature, and composition on solute association and conformational equilibria using the fluctuation theory of solutions are provided. The expressions are exact and can be used to interpret experimental or computer simulation data for any multicomponent mixture involving molecules of any size and character at any composition. The relationships involve particle-particle, particle-energy, and energy-energy correlations within local regions in the vicinity of each species involved in the equilibrium. In particular, it is demonstrated that the results can be used to study peptide and protein association or aggregation, protein denaturation, and protein-ligand binding. Exactly how the relevant fluctuating properties may be obtained from experimental or computer simulation data are also outlined. It is shown that the enthalpy, heat capacity, and compressibility differences associated with the equilibrium process can, in principle, be obtained from a single simulation. Fluctuation based expressions for partial molar heat capacities, thermal expansions, and isothermal compressibilities are also provided.

Partial Molar Isentropic and Isothermal Compressions of the Nucleosides Adenosine, Cytidine, and Uridine in Aqueous Solution at 298.15 K

Sound speeds have been measured for aqueous solutions of the nucleosides adenosine, cytidine, and uridine at T = 298.15 K and at ambient pressure. For adenosine and uridine, the partial molar isentropic compressions at infinite dilution, KS,2o, were derived from the sound speed data using conventional methods. These KS,2o results were combined with the partial molar heat capacities and partial molar isobaric expansions at infinite dilution available from the literature to evaluate, for the first time, the partial molar isothermal compressions at infinite dilution, KT,2o {KT,2o = −(∂V2o/∂p)T, where V2o is the partial molar volume of the solute at infinite dilution}. An alternative method is described for the calculation of the KS,2o and KT,2o values for cytidine from the sound speed data. The KT,2o results for the nucleosides have been rationalized in terms of the likely solute−water interactions. For cytidine, an analysis of the molality dependence of the partial molar isothermal compression in terms of self-association has also been explored.

High-pressure EPR reveals conformational equilibria and volumetric properties of spin-labeled proteins.

Identifying equilibrium conformational exchange and characterizing conformational substates is essential for elucidating mechanisms of function in proteins. Site-directed spin labeling has previously been employed to detect conformational changes triggered by some event, but verifying conformational exchange at equilibrium is more challenging. Conformational exchange (microsecond-millisecond) is slow on the EPR time scale, and this proves to be an advantage in directly revealing the presence of multiple substates as distinguishable components in the EPR spectrum, allowing the direct determination of equilibrium constants and free energy differences. However, rotameric exchange of the spin label side chain can also give rise to multiple components in the EPR spectrum. Using spin-labeled mutants of T4 lysozyme, it is shown that high-pressure EPR can be used to: (i) demonstrate equilibrium between spectrally resolved states, (ii) aid in distinguishing conformational from rotameric exchange as the origin of the resolved states, and (iii) determine the relative partial molar volume (ΔV°) and isothermal compressibility (Δβ(T)) of conformational substates in two-component equilibria from the pressure dependence of the equilibrium constant. These volumetric properties provide insight into the structure of the substates. Finally, the pressure dependence of internal side-chain motion is interpreted in terms of volume fluctuations on the nanosecond time scale, the magnitude of which may reflect local backbone flexibility.

Thermodynamic properties of peptide solutions 19. Partial molar isothermal compressions at T = 298.15 K of some peptides of sequence gly-X-gly in aqueous solution

The partial molar isobaric expansions at infinite dilution and T = 298.15 K, E 2 ∘ { E 2 ∘ = ( ∂ V 2 ∘ / ∂ T ) p } were determined recently for some tripeptides of sequence glycyl-X-glycine, where X is one of the amino acids alanine, valine, leucine, isoleucine, phenylalanine, methionine, proline, serine, threonine, asparagine, glutamine, histidine, and tyrosine. These quantities, along with partial molar heat capacity data available from the literature, were used to convert the partial molar isentropic compressions at infinite dilution determined previously for these tripeptides into the partial molar isothermal compressions at infinite dilution and T = 298.15 K, K T , 2 ∘ { K T , 2 ∘ = - ( ∂ V 2 ∘ / ∂ p ) T } . These K T , 2 ∘ results, along with that for triglycine, were used to estimate the contributions of the amino acid side-chains to the partial molar isothermal compressions of peptides. The side-chain contributions have been rationalized in terms of the likely peptide–water interactions.