Hydration free energies and entropies for water in protein interiors

Free energy calculations for the transfer of a water molecule from the pure liquid to an interior cavity site in a protein are presented. Two different protein cavities, in bovine pancreatic trypsin inhibitor (BPTI) and in the I76A mutant of barnase, represent very different environments for the water molecule: one which is polar, forming four water-protein hydrogen bonds, and one which is more hydrophobic, forming only one water-protein hydrogen bond. The calculations give very different free energies for the different cavities, with only the polar BPTI cavity predicted to be hydrated. The corresponding entropies for the transfer to the interior cavities are calculated as well and show that the transfer to the polar cavity is significantly entropically unfavorable while the transfer to the nonpolar cavity is entropically favorable. For both proteins an analysis of the fluctuations in the positions of the protein atoms shows that the addition of a water molecule makes the protein more flexible. This increased flexibility appears to be due to an increased length and weakened strength of protein-protein hydrogen bonds near the cavity.     

Evaluation of intrinsic compressibility of proteins by molecular dynamics simulation

Molecular dynamics simulation has been performed on five native proteins in water to evaluate their intrinsic isothermal compressibilities beta(T,int). To identify physical factors contributing to protein compressibility, a general method is presented for analyzing the compressibility of mechanically inhomogeneous systems. The value of beta(T,int) varies with protein species considerably: beta-lactoglobulin (14.15 x 10(-2) GPa(-1)) is more than twice as compressible as ribonuclease A (6.77 x 10(-2) GPa(-1)). Beta-lactoglobulin and myoglobin (13.95 x 10(-2) GPa(-1)) have similar values of beta(T,int), but the mechanisms responsible for them are significantly different. The volume fluctuations of internal cavities and the magnitudes of the crosscorrelation between them are the key factors determining beta(T,int) of proteins. Though the volume fractions of internal cavity for the five studied proteins are nearly equal to one another, the mean cavity compressibilities beta(T,cav) vary considerably with protein species and range from 0.35 to 0.69 GPa(-1), which are much smaller than those of normal organic liquids such as methanol, ethanol, and benzene and close to that of glycerol (0.55 GPa(-1)), a strongly associated liquid.     

Hydrophobic effects on partial molar volume

The hydrophobic effects on partial molar volume (PMV) are investigated as a PMV change in the transfer of a benzenelike nonpolar solute from the nonpolar solvent to water, using an integral equation theory of liquids. The volume change is divided into two effects. One is the "packing" effect in the transfer from the nonpolar solvent to hypothetical "nonpolar water" without hydrogen bonding networks. The other is the "iceberg" effect in the transfer from nonpolar water to water. The results indicate that the packing effect is negative and a half compensated by the positive iceberg effect. The packing effect is explained by the difference in the solvent compressibility. Further investigation shows that the sign and magnitude of the volume change depend on the solute size and the solvent compressibility. The finding gives a significant implication that the exposure of a hydrophobic residue caused by protein denaturation can either increase or decrease the PMV of protein depending on the size of the residue and the fluctuation of its surroundings.     

Cavities in molecular liquids and the theory of hydrophobic solubilities

Thermal configurational data on neat liquids are used to obtain the work of formation of hard spherical cavities of atomic size in six molecular solvents: n-hexane, n-dodecane, n-undecyl alcohol, chloroform, carbon tetrachloride, and water. These results are used to test a recent suggestion that the differences between nonaqueous solvents and liquid water in solvation of inert gases are not principally due to the hydrogen-bonded structure of liquid water but rather to the comparatively small size of the water molecule. The frequencies of occurrence of cavities in liquid water can be meaningfully distinguished from those in the organic solvents. Liquid water has a larger fractional free volume, but that free volume is distributed in smaller packets. With respect to cavity work, water is compared to a solvent of the same molecular density and composed of hard spheres of the same size as the water molecule. That comparison indicates that the hard-sphere liquid finds more ways to configure its free volume in order to accommodate an atomic solute of substantial size and thus, would be more favorable solvent for inert gases. The scaled particle model of inert gas solubility in liquid water predicts cavity works 20% below the numerical data for TIP4P water at 300 K and 1.0 g/cm3 for cavity radii near 2.0 angstroms. It is argued that the sign of this difference is just the sign that ought to be expected and that the magnitude of this difference measures structural differences between water and the directly comparable hard-sphere liquid. In conjunction with previous data, these results indicate that atomic sized cavities should be considered submacroscopic.     

An analysis of molecular packing and chemical association in liquid water using quasichemical theory

We calculate the hydration free energy of liquid TIP3P water at 298 K and 1 bar using a quasi-chemical theory framework in which interactions between a distinguished water molecule and the surrounding water molecules are partitioned into chemical associations with proximal (inner-shell) waters and classical electrostatic-dispersion interactions with the remaining (outer-shell) waters. The calculated free energy is found to be independent of this partitioning, as expected, and in excellent agreement with values derived from the literature. An analysis of the spatial distribution of inner-shell water molecules as a function of the inner-shell volume reveals that water molecules are preferentially excluded from the interior of large volumes as the occupancy number decreases. The driving force for water exclusion is formulated in terms of a free energy for rearranging inner-shell water molecules under the influence of the field exerted by outer-shell waters in order to accommodate one water molecule at the center. The results indicate a balance between chemical association and molecular packing in liquid water that becomes increasingly important as the inner-shell volume grows in size.     

Negative linear compressibility in confined dilatating systems

The role of a matrix response to a fluid insertion is analyzed in terms of a perturbation theory and Monte Carlo simulations applied to a hard sphere fluid in a slit of fluctuating density-dependent width. It is demonstrated that a coupling of the fluid-slit repulsion, spatial confinement, and the matrix dilatation acts as an effective fluid-fluid attraction, inducing a pseudocritical state with divergent linear compressibility and noncritical density fluctuations. An appropriate combination of the dilatation rate, fluid density, and the slit size leads to the fluid states with negative linear compressibility. It is shown that the switching from positive to negative compressibility is accompanied by an abrupt change in the packing mechanism.     

Contrasting nonaqueous against aqueous solvation on the basis of scaled-particle theory

Normal hexane is adopted as a typical organic solvent for comparison with liquid water in modern theories of hydrophobic hydration, and detailed results are worked-out here for the C-atom density in contact with a hard-sphere solute, rhoCG(R), for the full range of solute radii. The intramolecular structure of an n-hexane molecule introduces qualitative changes in G(R) compared to scaled-particle models for liquid water. Also worked-out is a revised scaled-particle model implemented with molecular simulation results for liquid n-hexane. The classic scaled-particle model, acknowledging the intramolecular structure of an n-hexane molecule, is in qualitative agreement with the revised scaled-particle model results, and is consistent in sizing the methyl/methylene sites which compose n-hexane in the simulation model. The classic and revised scaled-particle models disagree for length scales greater than the radius of a methyl group, however. The liquid-vapor surface tension of n-hexane predicted by the classic scaled-particle model is too large, though the temperature variation is reasonable; this contrasts with the classic scaled-particle theory for water which predicts a reasonable magnitude of the water liquid-vapor surface tension, but an incorrect sign for the temperature derivative at moderate temperatures. Judging on the basis of the arbitrary condition that drying is indicated when G(R)<1, hard spheres dry at smaller sizes in n-hexane than in liquid water.     

Hydrophobic interaction chromatography of proteins. I. The effects of protein and adsorbent properties on retention and recovery

The contributions of protein and adsorbent properties to retention and recovery were examined for hydrophobic interaction chromatography (HIC) using eight commercially available phenyl media and five model proteins (ribonuclease A, lysozyme, alpha-lactalbumin, ovalbumin and BSA). The physical properties of the adsorbents were determined by inverse size exclusion chromatography (ISEC). The adsorbents examined differ from each other in terms of base matrix, ligand density, porosity, mean pore radius, pore size distribution (PSD) and phase ratio, allowing systematic studies to understand how these properties affect protein retention and recovery in HIC media. The proteins differ in such properties as adiabatic compressibility and molecular mass. The retention factors of the proteins in the media were determined by isocratic elution. The results show a very clear trend in that proteins with high adiabatic compressibility (higher flexibility) were more strongly retained. For proteins with similar adiabatic compressibilities, those with higher molecular mass showed stronger retention in Sepharose media, but this trend was not observed in adsorbents with polymethacrylate and polystyrene divinylbenzene base matrices. This observation could be related to protein recovery, which was sensitive to protein flexibility, molecular size, and conformation as well as the ligand densities and base matrices of the adsorbents. Low protein recovery during isocratic elution could affect the interpretation of protein selectivity results in HIC media. The retention data were fitted to a previously published retention model based on the preferential interaction theory, in terms of which retention is driven by release of water molecules and ions upon protein-adsorbent interaction. The calculated number of water molecules released was found to be statistically independent of protein retention strength and adsorbent and protein properties.     

On the cavitation and pore blocking in slit-shaped ink-bottle pores

We present GCMC simulations of argon adsorption in slit pores of different channel geometry. We show that the isotherm for an ink-bottle pore can be reconstructed as a linear combination of the local isotherms of appropriately chosen independent unit cells. Second, depending on the system parameters and operating conditions, the phenomena of cavitation and pore blocking can occur for a given configuration of the ink-bottle pore by varying the geometrical aspect ratio. Although it has been argued in the literature that the geometrical aspects of the system govern the evaporation mechanism (either cavitation or pore blocking), we here put forward an argument that the local compressibility in different parts of the ink-bottle pore is the deciding factor for evaporation. When the fluid in the small neck is strongly bound, cavitation is the governing process, and molecules in the cavity evaporate to the surrounding bulk gas via a mass transfer mechanism through the pore neck. When the pore neck is sufficiently large, the system of neck and cavity evaporates at the same pressure, which is a consequence of the comparable compressibility between the fluid in the neck and that in the cavity. This suggests that local compressibility is the measure of cohesiveness of the fluid prior to evaporation. One consequence that we derive from the analysis of isotherms of a number of connected pores is that by analyzing the adsorption branch or the desorption branch of an experimental isotherm may not lead to the correct pore sizes and the correct pore volume distribution.     

High-performance liquid chromatography of proteins using chemically-modified silica supports

Summary Highly efficient and fast exclusion-chromatographic separations of proteins are possible on chemically-modified, silica stationary phases. By optimizing the pH and the ionic strength of the aqueous eluent secondary interactions of the samples with surface groups can be excluded. Bonded propylamide groups proved to possess optimum properties for exclusion chromatography. With other functional groups adsorption effects cannot be excluded totally. The optimum pore size distribution for protein separation up to relative molecular masses of 500,000 daltnons is between 10nm and 50nm. With these silica-based phases the pore size distribution, the pore volume and the packing characteristics are independent of the eluent, therefore the same column can be used with aqueous as well with organic eluents. It is possible to correlate the elution volume (molecular size) of proteins with those of polystyrene standars. The recovery of the proteins and their biological activity has always been better than 90%. The potentialities of adsorption chromatography of proteins on chemically-bonded stationary plases with different functional groups are demonstrated.     

Molecular dynamics study of the n-hexane-water interface: towards a better understanding of the liquid-liquid interfacial broadening

By molecular dynamics simulations, we have studied the hydrophilic-hydrophobic interface between water and n-hexane liquid phases. For all temperatures studied our computed interfacial tension agrees very well with the experimental value. However, the interfacial width calculated from capillary wave theory systematically overestimates the width obtained from fitting either the total density or composition profile. We rationalize the applicability of capillary wave theory for our system by reconsidering the usual value taken for the correlation length. This is motivated by the presence of order at the interface. Possible implications for recent experimental studies on the structure of model alkane-water interfaces are discussed, including the significance of the intrinsic width parameter.     

液相色谱/四极杆-飞行时间质谱法筛查奶酪中29种禁用和限用合成色素

建立了奶酪样品中29种禁用和限用合成色素的液相色谱/四极杆-飞行时间质谱(LC/Q-TOF MS)筛查方法。样品经正己烷-水(3:1, v/v)振荡提取,得到正己烷层、水层和残渣3部分。正己烷层经旋转蒸发浓缩后,用乙酸乙酯-环己烷(1:1, v/v)溶解,经过凝胶渗透色谱(GPC)净化去除油脂。水层经乙腈振荡提取,得到乙腈-水提取液。残渣经氨水-甲醇(1:99, v/v)溶液振荡提取,得到氨水-甲醇提取液。乙腈-水提取液和氨水-甲醇提取液不需净化直接分析。结果表明: 29种不同极性范围的合成色素化合物分别得到了有效的提取,提取回收率为70%～95%。而Q-TOF MS提供的精确质量数定性功能可以将不同种类的合成色素化合物筛查出来,各化合物与精确质量质谱库中化合物的匹配度为59.66～99.47。通过Target MS/MS扫描方式进行定量,得到8种苏丹类化合物的方法检出限为0.4～2.5 μg/kg, 21种水溶性合成色素及染料化合物的检出限为20～80 μg/kg。该方法对禁用和限用合成色素的筛查范围广泛,对含有蛋白质、脂肪等基质的食品具有较好的适用性。     

Investigation of mechanical properties of insulin crystals by atomic force microscopy

Mechanical properties of protein crystals and aggregates depend on the conformational and structural properties of individual protein molecules as well as on the packing density and structure within solid materials. An atomic force microscopy (AFM)-based approach is developed to measure the elastic modulus of small protein crystals by nanoindentation and is applied to measure the elasticity of insulin crystals. The top face of the crystals deposited on mica substrates is identified as the (001) face. Insulin crystals exhibit a nearly elastic response during the compression cycle. The elastic modulus measured on the top face has asymmetric distribution with a significant width. This width is related to the uncertainty in the deflection sensitivity. A model that takes into account the distribution of the sensitivity values is used to correct the elastic modulus. Measurements performed in aqueous buffer on several crystals at different locations with three different AFM probes give a mean elastic modulus of 164 +/- 10 MPa. This value is close to the static elastic moduli of other protein crystals measured by different techniques that are usually measured in the range from 100 MPa to 1 GPa. The measured modulus of insulin crystals falls between the elastic modulus values of insulin amyloid fibrils measured previously at two orthogonal directions (a modulus of 14 MPa was measured by compressing the fibril in the direction perpendicular to the fibril axis, and a modulus of 3.3 GPa was measured in the direction along the fibril axis). This comparison indicates the heterogeneous structure of fibrils in the direction perpendicular to the fibril axis, with a packing density of the amyloid fibril core that is higher than the average packing density in insulin crystals. The mechanical wear of insulin crystals is detected during AFM measurements. In nanoindentation experiments on insulin crystal, the compressive load by the AFM tip ( approximately 1 nN, corresponding to a pressure of around 5 MPa) occasionally removes protein molecules from the top or the second top layer of insulin crystal in a sequential manner. The molecular model of this surface damage is proposed. In addition, the removal of the multiple layers of molecules is observed during the AC-mode imaging in aqueous buffer. The number of removed layers depends on the scan size.     

Effect of temperature on mixing thermodynamics of a new ionic liquid: {2-Hydroxy ethylammonium formate (2-HEAF) + short hydroxylic solvents}

Density and ultrasonic velocity of the mixtures of the new ionic liquid 2-hydroxy ethylammonium formate (2-HEAF) and short hydroxylic solvents (water, methanol, and ethanol) have been measured at the range of temperature (288.15 to 323.15) K and atmospheric pressure. The corresponding apparent molar volume and the apparent molar isentropic compressibility values have been evaluated from the experimental data and fitted to a temperature dependent Redlich–Mayer equation. From these correlations, the limiting infinite dilution values of the apparent magnitudes have also been computed. Derived properties such as isobaric expansibility and isothermal coefficient of pressure excess molar enthalpy were computed due to their importance in the study of specific molecular interactions. The new experimental data were used to test the capability of prediction of the modified Heller temperature dependent equation (MHE) and collision factor theory (CFT). The obtained results indicate that ionic liquid interactions in water are weaker than in the studied alcoholic solutions. An intersection point in isotherms of isentropic compressibility was observed for aqueous solutions which may be an indication of the clathrate structural interactions at high solvent composition. The observed inverse dependence on temperature for aqueous or alcoholic mixtures points out the special trend of packing of this ionic liquid into hydroxylic solvents and its strong dependence on steric hindrance of aliphatic residues. As previously observed, the increase in van der Waals forces due to the presence of long alkyl chain (into ionic liquid and alcohols) leads to higher interactions on mixing.     

Pairwise interactions between linear alkanes in water measured by AFM force spectroscopy

Pairwise interactions between n-alkanes from decane to octadecane in water have been studied by single-molecule force spectroscopy. The interacting molecules are covalently tethered to the glass substrate and to the probe of an atomic force microscope by water-soluble linkers to facilitate single-molecule detection. However, the measured distribution of rupture forces deviates significantly from the distribution predicted by theoretical models for rupture of individual bonds. To describe the statistics of rupture forces, an analytical model that considers near-simultaneous rupture of two bonds loaded by tethers with different lengths is introduced. The common most probable force analysis approach is used for comparison. In both data analyses, the possible systematic errors due to nonlinear elasticity of polymeric tethers and variations in the shape of the potential of mean force were considered. Experimental distributions of rupture forces are well-fit by the two-bond rupture model using a single set of kinetic parameters for different experiments, while the most probable force approach yields parameters that vary significantly for different samples. The measured activation energies for dissociation of alkanes are close to the free energies predicted by cavity models of hydrophobic interactions. The surface free-energy density is estimated to be approximately 21 kJ/(mol nm (2)) and is close to the upper limit of free energies used in the computer simulations of hydrophobic interactions in proteins. In contrast to the predictions of the cavity models, the measured activation energy does not increase monotonically with increase in alkane chain size. To explain this discrepancy and the measured distance to the transition-state barrier (approximately 0.6 nm), it is suggested that alkanes undergo conformational transition to the collapsed state upon dimerization. Change in the alkane conformation from extended to helical has been observed previously for binding of alkanes in water to hydrophobic synthetic receptors. Here, however, conformational change is suggested without geometrical constraints imposed by small cavitands. The proposed collapsed state of the alkane dimers has implications for the kinetics of self-assembly of surfactant micelles.     

Fluorescence lifetime distribution of folded and unfolded proteins

Time-resolved fluorescence of single tryptophan proteins have demonstrated the complexity of protein dynamic and protein structure. In particular, for some single tryptophan proteins, their fluorescence decay is best described by a distribution of fluorescence lifetimes rather than one or two lifetimes. Such results have provided further confirmation that the protein system is one which fluctuates between a hierarchy of many conformational substates. With this scenario as a theoretical framework, the correlations between protein dynamic and structure are investigated by studying the time-resolved fluorescence and anisotropy decay of holo and apo human superoxide dismutase (HSOD) at different denaturant concentrations. As a function of guanidine hydrochloride (GdHCl), the width of the fluorescence lifetime distribution of HSOD displays a maximum which is not coincident with the fully denatured form of HSOD at 6.5M GdHCl. Furthermore, the width of the fluorescence lifetime distribution for the fully denatured forms of holo and apo HSOD is greater than that of the native forms.     

Influence of pressure on the properties of chromatographic columns. II. The column hold-up volume

The effect of the local pressure and of the average column pressure on the hold-up column volume was investigated between 1 and 400 bar, from a theoretical and an experimental point of view. Calculations based upon the elasticity of the solids involved (column wall and packing material) and the compressibility of the liquid phase show that the increase of the column hold-up volume with increasing pressure that is observed is correlated with (in order of decreasing importance): (1) the compressibility of the mobile phase (+1 to 5%); (2) in RPLC, the compressibility of the C18-bonded layer on the surface of the silica (+0.5 to 1%); and (3) the expansion of the column tube (<0.001%). These predictions agree well with the results of experimental measurements that were performed on columns packed with the pure Resolve silica (0% carbon), the derivatized Resolve-C18 (10% carbon) and the Symmetry-C18 (20% carbon) adsorbents, using water, methanol, or n-pentane as the mobile phase. These solvents have different compressibilities. However, 1% of the relative increase of the column hold-up volume that was observed when the pressure was raised is not accounted for by the compressibilities of either the solvent or the C18-bonded phase. It is due to the influence of the pressure on the retention behavior of thiourea, the compound used as tracer to measure the hold-up volume.     

Protein unfolding, amyloid fibril formation and configurational energy landscapes under high pressure conditions

High hydrostatic pressure induces conformational changes in proteins ranging from compression of the molecules to loss of native structure. In this tutorial review we describe how the interplay between the volume change and the compressibility leads to pressure-induced unfolding of proteins and dissociation of amyloid fibrils. We also discuss the effect of pressure on protein folding and free energy landscapes. From a molecular viewpoint, pressure effects can be rationalised in terms of packing and hydration of proteins.