Comment on “Determination of the quaternary phase diagram of the water–ethylene glycol–sucrose–NaCl system and a comparison between two theoretical methods for synthetic phase diagrams” Cryobiology 61 (2010) 52–57

Recently, measurements of a considerable portion of the phase diagram for the quaternary system water–ethylene glycol–sucrose–NaCl were published (Han et al., 2010). In that article, the data were used to evaluate the accuracy of two non-ideal multi-solute solution theories: the Elliott et al. form of the multi-solute osmotic virial equation and the Kleinhans and Mazur freezing point summation model. Based on this evaluation, it was concluded that the freezing point summation model provides more accurate predictions for the water–ethylene glycol–sucrose–NaCl system than the multi-solute osmotic virial equation. However, this analysis suffered from a number of issues, notably including the use of inconsistent solute-specific coefficients for the multi-solute osmotic virial equation. Herein, we reanalyse the data using a recently-updated and consistent set of solute-specific coefficients (Zielinski et al., 2014). Our results indicate that the two models have very similar performance, and, in fact, the multi-solute osmotic virial equation can provide more accurate predictions than the freezing point summation model depending on the concentration units used.     

Application of the osmotic virial equation in cryobiology

The multisolute osmotic virial equation is the only multisolute thermodynamic solution theory that has been derived from first principles and can make predictions of multisolute solution behaviour in the absence of multisolute solution data. Other solution theories either (i) include simplifying assumptions that do not take into account the interactions between different types of solute molecules or (ii) require fitting to multisolute data to obtain empirical parameters. The osmotic virial coefficients, which are obtained from single-solute data, can be used to make predictions of multisolute solution osmolality. The osmotic virial coefficients for a range of solutes of interest in cryobiology are provided in this paper, for use with concentration units of both molality and mole fraction, along with an explanation of the background and theory necessary to implement the multisolute osmotic virial equation.     

Evaluation of second osmotic virial coefficients from molecular simulation following scaled-particle theory

ABSTRACT

We report a scaled particle theory-based method for evaluation of second osmotic virial coefficients from molecular simulations of dilute species in solution. In this method, we evaluate the work associated with growing a cavity in solution that is perfectly permeable to the solvent but is completely impermeable to the solutes, thereby establishing an osmotic stress between the cavity interior and exterior. Extrapolating our results to determine the solute concentration in contact with a cavity with an infinite radius, we are able to evaluate the solute osmotic pressure and second osmotic virial coefficient. A finite size correction is introduced to account for the impact of effectively concentrating the solutes in the periphery of the simulation box with increasing cavity size. We demonstrate the utility of the proposed method by evaluating second osmotic virial coefficients for methane in water as a function of temperature. The approach proposed here provides a physically transparent route for calculation of second osmotic virial coefficients by direct interrogation of simulation configurations without having to explicitly evaluate the long-range integral over solute-solute correlations required following McMillan-Mayer theory.     

Two applications of the thermogram of the alcohol/water binary system with compositions of cryobiological interests

Quantitative analyses of the bound water content in the alcohol aqueous solution and its osmotic behavior should be cryobiologically significant. This paper has presented two applications of the thermogram of the alcohol/water system recorded by differential scanning calorimeter (DSC). Both applications are: (1) generating the quantitative relationship between the bound water content and the solution composition; (2) calculating the osmotic virial coefficients for alcohols. Five alcohols including methanol, ethanol, ethylene glycol, propylene glycol and glycerol are investigated. In the present study, partial binary phase diagrams of these five alcohol solutions are determined in the first place. The bound water contents in these solutions are quantitatively evaluated by three criteria afterwards. In the end, the osmotic virial coefficients for these alcohols are calculated according to the osmotic virial equation. It is turned out that the bound water fraction out of the total water content increases with a rising molality. The ability of the solute to restrict water molecules can be weakened when the solution becomes more concentrated. The results also indicate that propylene glycol should be the strongest “water-blocker” while methanol the weakest one. These findings can deepen our understanding of the cryoprotective properties of the alcohols from the perspectives of their roles in binding free water and promoting the osmotic efflux of cell water.     

Nonequivalence of second virial coefficients from sedimentation equilibrium and static light scattering studies of protein solutions

Experimental data for ovalbumin and lysozyme are presented to highlight the nonequivalence of second virial coefficients obtained for proteins by sedimentation equilibrium and light scattering. Theoretical considerations confirm that the quantity deduced from sedimentation equilibrium distributions is B(22), the osmotic second virial coefficient describing thermodynamic nonideality arising solely from protein self-interaction. On the other hand, the virial coefficient determined by light scattering is shown to reflect the combined contributions of protein-protein and protein-buffer interactions to thermodynamic nonideality of the protein solution. Misidentification of the light scattering parameter as B(22) accounts for published reports of negative osmotic second virial coefficients as indicators of conditions conducive to protein crystal growth. Finally, textbook assertions about the equivalence of second virial coefficients obtained by sedimentation equilibrium and light scattering reflect the restriction of consideration to single-solute systems. Although sedimentation equilibrium distributions for buffered protein solutions are, indeed, amenable to interpretation in such terms, the same situation does not apply to light scattering measurements because buffer constituents cannot be regarded as part of the solvent: instead they must be treated as non-scattering cosolutes.     

An approach to the study of phase separation in ternary aqueous systems

1. Simple thermodynamic expressions are used to describe the properties of uncharged binary and ternary polymer solutions, in particular the sedimentation equilibrium of binary systems and the osmotic pressures and `incompatible' phase separations of ternary systems. 2. Sedimentation-equilibrium experiments were performed on four samples of dextran and two of polyethylene glycol. The critical points of the phase diagrams were determined for the mixed solutions of polyethylene glycol–dextran–water and of polyethylene glycol–bovine serum albumin–0·2m-sodium chloride solution. Osmotic pressures were measured on a single-phase mixed solution of a polyethylene glycol and a dextran. By use of the simple thermodynamic expressions consistent values of second virial and interaction coefficients for the materials used were obtained from these experiments. 3. The interpretation of the values of the second virial and interaction coefficients, on the basis of three models of molecular interaction, is discussed.     

Canine RBC osmotic tolerance and membrane permeability

The objective of this study was to determine the cryobiological characteristics of canine red blood cells (RBC). These included the hydraulic conductivity (L(p)), the permeability coefficients (P(s)) of common cryoprotectant agents (CPAs), the associated reflection coefficient (sigma), the activation energies (E(a)) of L(p) and P(s) and the osmotic tolerance limits. By using a stopped-flow apparatus, the changes of fluorescence intensity emitted by intracellularly entrapped 5-carboxyfluorescein diacetate (CFDA) were recorded when cells were experiencing osmotic volume changes. After the determination of the relationship between fluorescence intensity and cell volume, cell volume changes were calculated. These volume changes were used in three-parameter fitting calculations to determine the values of L(p), P(s), and sigma for common CPAs. These volume measurements and data analyses were repeated at three different temperatures (22, 14, 7 degrees C). Using the Arrhenius equation, the activation energies of L(p) and P(s) in the presence of CPAs were determined. The osmotic tolerance limits for canine RBC were determined by measuring the percentage of free hemoglobin in NaCl solutions with various osmolalities compared to that released by RBC incubated in double distilled water. The upper and lower osmotic tolerance limits were found to be 150mOsm (1.67V(iso)) and 1200mOsm (0.45V(iso)), respectively. These parameters were then used to calculate the amount of non-permeating solute needed to keep cell volume excursions within the osmotic tolerance limits during CPA addition and removal.     

Exclusion in hyaluronate gels.

Osmotic pressures of solutions of hyaluronate (HA) (mol wt 117,000) and mixtures of HA and bovine serum albumin (BSA) in phosphate-buffered saline, pH 7.2 were measured with a membrane osmometer. The data were fit with a virial expansion in integral powers of total nondiffusible solute concentration. Values of number average molecular weight were calculated for HA and the mixtures from the first virial coefficients. The excluded volume of HA in the single nondiffusible solute solution was calculated from the second virial coefficient extracted from the data on the HA solution. The excluded volume of HA with respect to BSA was estimated from the "osmotic parameters" of HA and BSA by an approach developed in 1976 by Shaw. The resulting excluded volume of HA with respect to BSA was compared with those obtained from a lightly cross-linked HA gel and from solutions of HA (mol wt 1.5 x 10(6)) studied in 1964 by Laurent. The development of this cross-linked HA gel and its subsequent calibration are described.     

An artificial osmotic cell: a model system for simulating osmotic processes and for studying phenomena of negative pressure in plants

Abstract An artificial osmotic cell has been constructed using reverse osmosis membranes. The cell consisted of a thin film of an osmotic solution (thickness: 100 to 200 μm) containing a non-permeating solute and was bounded between the membrane and the front plate of a pressure transducer which continuously recorded cell turgor. The membrane was supported by metal grids to withstand positive and negative pressures (P). At maximum, negative pressures of up to –0.7 MPa (absolute) could be created within the film on short-term and pressures of up to –0.3 MPa could be maintained without cavitation for several hours. As with living plant cells, the application of osmotic solutions of a non-permeating solute resulted in monophasic relaxations of turgor pressure from which the hydraulic conductivity of the membrane (Lp) and the elastic modulus of the cell (?) could be estimated. The application of solutions with permeating solutes resulted in biphasic pressure relaxation curves (as for living cells) from which the permeability (P_s) and reflection (σ_s) coefficients could be evaluated for the given membrane. Lp, P_s, and σ_s were independent of P and did not change upon transition from the positive to the negative range of pressure. It is concluded that the artificial cell could be used to simulate certain transport properties of living cells and to study phenomena of negative pressure as they occur in the xylem and, perhaps, also in living cells of higher plants.     

Effect of solution non-ideality on erythrocyte volume regulation

A non-ideal, hydrated, non-dilute pseudo-binary salt-protein-water solution model of the erythrocyte intracellular solution is presented to describe the osmotic behavior of human erythrocytes. Existing experimental activity data for salts and proteins in aqueous solutions are used to formulate van Laar type expressions for the solvent and solute activity coefficients. Reasonable estimates can therefore be made of the non-ideality of the erythrocyte intracellular solution over a wide range of osmolalities. Solution non-ideality is shown to affect significantly the degree of solute polarization within the erythrocyte intracellular solution during freezing. However, the non-ideality has very little effect upon the amount of water retained within erythrocytes cooled at sub-zero temperatures.     

pH control of the third virial coefficient of hyaluronate solutions calculated from van der Waals forces by means of the Lifshitz-McLachlan susceptibility theory

Positive third virial coefficients and osmotic coefficients have been calculated for human umbilical cord hyaluronic acid solutions at pHs 6.0, 6.5, 7.0, 7.5, 8.0, and 8.5 and constant ionic strength 0.1. The calculations are based on experimental axial flow birefringence and radial linear dichroism data previously reported and the Lifshitz-McLachlan field theory of van der Waals forces. The second virial coefficients are negative, according to both this analysis and light scattering evidence, and reflect the tendency of hyaluronic acid to associate. This negativity denies the assumption of force additivity required by virial expansion theory.The results are in reasonable agreement with those of light scattering studies, and indicate the extreme nonideality of hyaluronate solutions with a high degree of pH control of osmotic pressure. The data are explained within the context of statistical mechanical and field theories of van der Waals forces, and the osmotic pressure of a solution is related to its optical properties. The numerical method used offers a way of exploring the applicability of modern interparticle force theory to biological systems.     

Predictive crystallization of ribonuclease A via rapid screening of osmotic second virial coefficients

Important progress has been made in recent years toward developing a molecular-level understanding of protein phase behavior in terms of the osmotic second virial coefficient, a thermodynamic parameter that characterizes pairwise protein interactions. Yet there has been little practical application of this knowledge to the field of protein crystallization, largely because of the difficult and time-consuming nature of traditional techniques for characterizing protein interactions. Self-interaction chromatography has recently been proposed as a highly efficient method for measuring the osmotic second virial coefficient. The utility of the technique is examined in this work by characterizing virial coefficients for ribonuclease A under 59 solution conditions using several crystallization additives, including PEG, sodium chloride, ammonium sulfate, and propanol. The virial coefficient measurements show some counterintuitive trends and shed light on the previous difficulties in crystallizing ribonuclease A. Crystallization experiments at the corresponding solution conditions were conducted by using ultracentrifugal crystallization. Using this methodology, ribonuclease A crystals were obtained under conditions for which the virial coefficients fell within the "crystallization slot." Crystallographic characterization showed that the crystals diffract to high resolution. Metastable crystals were also obtained for conditions outside, but near, the "crystallization slot," and they could also be frozen and used to collect structural information.     

Osmotic Biosensors. How to Use a Characean Internode for Measuring the Alcohol Content of Beer

Isolated internodes of Chara corallina and Nitella flexilis have been used to determine the concentration of one passively permeating solute in the presence of non-permeating solutes. The technique was based on the fact that the shape of the peaks of the biphasic responses of cell turgor (as measured in a conventional way using the cell pressure probe) depended on the concentration and composition of the solution and on the permeability and reflection coefficients of the solutes. Peak sizes were proportional to the concentration of the permeating solute applied to the cell. Thus, using the selective properties of the cell membrane as the sensing element and changes of turgor pressure as the physical signal, plant cells have been used as a new type of biosensor based on osmotic principles. Upon applying osmotic solutions, the responses of cell turgor (P) exactly followed the P(t) curves predicted from the theory based on the linear force/flow relations of irreversible thermodynamics. The complete agreement between theory and experiment was demonstrated by comparing measured curves with those obtained by either numerically solving the differential equations for volume (water) and solute flow or by using an explicit solution of the equations. The explicit solution neglected the solvent drag which was shown to be negligible to a very good approximation. Different kinds of local beers (regular and de-alcoholized) were used as test solutions to apply the system for measuring concentrations of ethanol. The results showed a very good agreement between alcohol concentrations measured by the sensor technique and those obtained from conventional techniques (enzymatic determination using alcohol dehydrogenase or from measurement of the density and refraction index of beer). However, with beer as the test solution, the characean internodes did show irreversible changes of the transport properties of the membranes leading to a shift in the responses when cells were treated for longer than 1 h with diluted beer. The accuracy and sensitivity of the osmotic biosensor technique as well as its possible applications are discussed.     

Membrane permeability characteristics and osmotic tolerance limits of sea urchin (Evechinus chloroticus) eggs

Development of effective cryopreservation protocols relies on knowledge of the fundamental cryobiological characteristics for a particular cell type. These characteristics include osmotic behaviour, membrane permeability characteristics, and osmotic tolerance limits. Here, we report on measures of these characteristics for unfertilized and fertilised eggs of the sea urchin (Evechinus chloroticus). In NaCl solutions of varying osmolalities, sea urchin eggs behaved as ideal linear osmometers. The osmotically inactive volume (vb) was similar for unfertilized and fertilised eggs, 0.367+/-0.008 (mean+/-SE) and 0.303+/-0.007, respectively. Estimates of water solubility (Lp) and solute permeability (Ps) and their respective activation energies (Ea) for unfertilized and fertilised eggs were determined following exposure to cryoprotectant (CPA) solutions at different temperatures. Irrespective of treatment, fertilised eggs had higher values of Lp and Ps. The presence of a CPA decreased Lp. Among CPAs, solute permeability was highest for propylene glycol followed by dimethyl sulphoxide and then ethylene glycol. Measures of osmotic tolerance limits of the eggs revealed unfertilized eggs were able to tolerate volumetric changes of -20% and +30% of their equilibrium volume; fertilised eggs were able to tolerate changes +/-30%. Using membrane permeability data and osmotic tolerance limits, we established effective methods for loading and unloading CPAs from the eggs. The results of this study establish cryobiological characteristics for E. chloroticus eggs of use for developing an effective cryopreservation protocol. The approach we outline can be readily adapted for determining cryobiological characteristics of other species and cell types, as an aid to successful cryopreservation.     

Determination of Solute Permeability in Chara Internodes by a Turgor Minimum Method : Effects of External pH

The analysis of Sha'afi et al. (Sha'afi, Rich, Mickulecky, Solomon 1970 J Gen Physiol 55: 427-450) for determining solute permeability in red blood cells has been modified and applied to turgid plant cells. Following the addition of permeating solute to the external medium, a biphasic response of cell turgor can be measured with the pressure probe in isolated internodes of Chara corallina. After an initial decrease in turgor due to water flow (water phase), turgor increases due to the uptake of the solute (solute phase) until the original turgor is reattained. From the pressure/time course in the neighborhood of the minimum turgor, the permeability of the osmotic solute can be determined. The data obtained by the minimum method for rapidly permeating (ethanol, methanol) and slowly permeating (formamide, dimethylformamide) solutes are similar to those calculated from the half-time of pressure changes during the solute phase and to data obtained by other workers using radioactive tracers. The methods employing the pressure probe were applied to examine the effect of high pH (up to pH 11) on the membrane permeability. There appeared to be no effect of high pH on the permeability coefficients, reflection coefficients, and hydraulic conductivity.     

Direct allowance for the effects of thermodynamic nonideality in the quantitative characterization of protein self-association by osmometry

A procedure is described for the direct analysis of osmotic pressure data for reversibly dimerizing proteins that makes allowance for effects of thermodynamic nonideality on the statistical–mechanical basis of the potential-of-mean-force between molecules. Detailed consideration is also given to calculation of the magnitudes of the required virial coefficients. After illustration of the approach with analysis of simulated osmotic pressure data, the method is used to obtain dimerization constants from published osmotic pressure data for soybean proteinase inhibitor, hemoglobin and α-chymotrypsin.     

Virial coefficients of protein solutions

An osmometer capable of measuring protein osmotic pressures up to 100 cms. of mercury pressure has been described. The principle of the osmometer is to set a given pressure and to permit the protein concentration to equilibrate with the pressure. The higher virial osmotic coefficients of egg albumin in various electrolytes and in 1 m urea as well as a function of NaCl concentration are reported. The virial coefficients of bovine serum albumin and of bovine methemoglobin in 1 m NaCl are also given. It appears that the primary cause for the departure of the osmotic pressure from ideality is due to the covolumes of the proteins.     

Molecular origins of osmotic second virial coefficients of proteins.

The thermodynamic properties of protein solutions are determined by the molecular interactions involving both solvent and solute molecules. A quantitative understanding of the relationship would facilitate more systematic procedures for manipulating the properties in a process environment. In this work the molecular basis for the osmotic second virial coefficient, B22, is studied; osmotic effects are critical in membrane transport, and the value of B22 has also been shown to correlate with protein crystallization behavior. The calculations here account for steric, electrostatic, and short-range interactions, with the structural and functional anisotropy of the protein molecules explicitly accounted for. The orientational dependence of the protein interactions is seen to have a pronounced effect on the calculations; in particular, the relatively few protein-protein configurations in which the apposing surfaces display geometric complementarity contribute disproportionately strongly to B22. The importance of electrostatic interactions is also amplified in these high-complementarity configurations. The significance of molecular recognition in determining B22 can explain the correlation with crystallization behavior, and it suggests that alteration of local molecular geometry can help in manipulating protein solution behavior. The results also have implications for the role of protein interactions in biological self-organization.     

A mixture theory analysis for passive transport in osmotic loading of cells

The theory of mixtures is applied to the analysis of the passive response of cells to osmotic loading with neutrally charged solutes. The formulation, which is derived for multiple solute species, incorporates partition coefficients for the solutes in the cytoplasm relative to the external solution, and accounts for cell membrane tension. The mixture formulation provides an explicit dependence of the hydraulic conductivity of the cell membrane on the concentration of permeating solutes. The resulting equations are shown to reduce to the classical equations of Kedem and Katchalsky in the limit when the membrane tension is equal to zero and the solute partition coefficient in the cytoplasm is equal to unity. Numerical simulations demonstrate that the concentration-dependence of the hydraulic conductivity is not negligible; the volume response to osmotic loading is very sensitive to the partition coefficient of the solute in the cytoplasm, which controls the magnitude of cell volume recovery; and the volume response is sensitive to the magnitude of cell membrane tension. Deviations of the Boyle-van't Hoff response from a straight line under hypo-osmotic loading may be indicative of cell membrane tension.