Measurement of grouped intracellular solute osmotic virial coefficients

Models of cellular osmotic behaviour depend on thermodynamic solution theories to calculate chemical potentials in the solutions inside and outside the cell. These solutions are generally thermodynamically non-ideal under cryobiological conditions. The molality-based Elliott et al. form of the multi-solute osmotic virial equation is a solution theory which has been demonstrated to provide accurate predictions in cryobiological solutions, accounting for the non-ideality of these solutions using solute-specific thermodynamic parameters called osmotic virial coefficients. However, this solution theory requires as inputs the exact concentration of every solute in the solution being modeled, which poses a problem for the cytoplasm, where such detailed information is rarely available. This problem can be overcome by using a grouped solute approach for modeling the cytoplasm, where all the non-permeating intracellular solutes are treated as a single non-permeating “grouped” intracellular solute. We have recently shown (Zielinski et al., J Physical Chemistry B, 2017) that such a grouped solute approach is theoretically valid when used with the Elliott et al. model, and Ross-Rodriguez et al. (Biopreservation and Biobanking, 2012) have previously developed a method for measuring the cell type-specific osmotic virial coefficients of the grouped intracellular solute. However, the Ross-Rodriguez et al. method suffers from a lack of precision, which—as we demonstrate in this work—can severely impact the accuracy of osmotic model predictions under certain conditions. Thus, we herein develop a novel method for measuring grouped intracellular solute osmotic virial coefficients which yields more precise values than the existing method and then apply this new method to measure these coefficients for human umbilical vein endothelial cells.     

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.     

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.     

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.     

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.     

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.     

Partitioning of low molecular combination peptides in aqueous two-phase systems of poly(ethylene glycol) and dextran in the presence of small amounts of K2HPO4/KH2PO4 buffer at 293 K: experimental results and predictions

Buffered aqueous two-phase systems are effective extraction systems for separating amphoteric hydrocarbons like, for example, polypeptides from aqueous phases. The design and basic engineering of such processes requires the knowledge of the liquid-liquid equilibrium. The study presented here aims to contribute to the development of methods to predict the partitioning of peptides in aqueous two-phase systems. Experimental results are reported for the partitioning of small amounts ( approximately 0.001 g solute per gram of solution) of low molecular combination peptides of glycine, L-glutamic acid, L-phenylalanine, and L-lysine (9 dipeptides, gly-glu, gly-phe, gly-lys, glu-gly, phe-gly, phe-glu, lys-gly, lys-glu, lys-phe; 7 tripeptides, gly-gly-phe, gly-phe-gly, glu-gly-phe, phe-gly-gly, lys-gly-lys, lys-glu-gly, lys-phe-lys) in aqueous two-phase systems of high molecular weight dextran (molecular weight about 500,000) and poly(ethylene glycol) (molecular weight about 6,000 and 35,000, respectively) in the presence of small amounts (about 0.05 mol/kg) of K2HPO4/KH2PO4 buffer at about 293 K. The new data are compared to predictions. Partition coefficients are predicted applying a group contribution excess Gibbs energy model. The model is an osmotic virial equation. It uses surface fractions to encounter for the probability of interactions between solutes. All model parameters were taken from the literature. They were determined exclusively from experimental data for the phase forming systems and for the partitioning of amino acids and their di- and tripeptides (containing only a single amino acid), but no experimental data for the partitioning of combinations peptides were used. In most cases predicted partition coefficients agree favourably with the experimental data.     

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 activity coefficient model for proteins

Modeling of the properties of biochemical components is gaining increasing interest due to its potential for further application within the area of biochemical process development. Generally protein solution properties such as protein solubility are expressed through component activity coefficients which are studied here. The original UNIQUAC model is chosen for the representation of protein activity coefficients and, to the best of our knowledge, this is the first time it has been directly applied to protein solutions. Ten different protein-salt-water systems with four different proteins, serum albumin, alphacymotrypsin, beta-lactoglobulin and ovalbumin, are investigated. A root-mean-squared deviation of 0.54% is obtained for the model by comparing calculated protein activity coefficients and protein activity coefficients deduced from osmotic measurements through virial expansion. Model predictions are used to analyze the effect of salt concentrations, pH, salt types, and temperature on protein activity coefficients and also on protein solubility and demonstrate consistency with results from other references. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 65-71, 1997.     

Theory of aggregation in solution. I. General equations and application to the stacking of bases,nucleosides, etc.

Earlier theoretical work on aggregation in imperfect gases and in solutions of protein molecules is reformulated here in such a way as to be applicable to a number of aggregation systems in solution. The theory is most easily developed for an “osmotic” solution. It is exact, in principle, and in particular does not treat the aggregates as an ideal mixture as is usually done. If osmotic virial coefficients are diffcult to measure in a particular case, it is then necessary to relate these coefficients to properties of the more conventional “constant pressure” solution. An important special case is used as an example in the last three sections: The stacking of bases, nucleosides, etc., is represented by a statistical mecchanical model in which the aggregates resemble vertical stacks of checkers.     

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.     

Ionic and osmotic equilibria of human red blood cells treated with nystatin

Human red blood cells have been incubated in the presence of nystatin, which allows Na and K, as well as Cl and pH to equilibrate rapidly when cell volume is set with external impermeant sucrose. The intracellular mean ionic activity coefficients, relative to values in the extracellular solution, for KCl and NaCl are 1.01 +/- 0.02 and 0.99 +/- 0.02 (SD, n = 10), respectively, and are independent of external pH, pH o, and of [sucrose]o. With nystatin the dependence of red cell volume on [sucrose]o deviates from ideal osmotic behavior by as much as a factor of three. A virial equation for the osmotic coefficient, phi, of human hemoglobin, Hb, accounts for the cell volumes, and is the same as that which describes Adair's measurements of phi Hb for Hb isolated from sheep and ox bloods. In the presence of nystatin the slope of the acid-base titration curve of the cells is independent of cell volume, implying that the charge on impermeant cellular solutes is independent of Hb concentration at constant pH. By modifying the Jacobs-stewart equations (1947. J. Cell. Comp. Physiol. 30: 79--103) with the osmotic coefficients of Hb and of salts, a nonideal thermodynamic model has been devised which predicts equilibrium Donnan ratios and red cell volume from the composition of the extracellular solution and from certain parameters of the cells. In addition to accounting for the dependence of cell volume on osmotic pressure, the model also describes accurately the dependence of Donnan ratios and cell volumes on pHo either in the presence or absence of nystatin.     

Donnan membrane equilibrium,sedimentation equilibrium,and coil expansion of DNA in salt solutions

This is a review of applications of the McMillan-Mayer-Hill virial theory and the ionic double-layer theory to dilute colloidal solutions, in particular, solutions of DNA. Interactions of highly charged colloidal rods are developed in terms of the second virial coefficients between two rods, and between one rod and one small co-ion. The relevant cluster integrals are evaluated with interaction potentials based on the Poisson-Boltzmann equation. The treatment is extended to the intrachain repulsion responsible for the statistical swelling of coiled DNA (excluded volume effect). The theory is compared with three sets of experimental data: The salt distribution in Donnan membrane equilibria of DNA-salt solutions, sedimentation equilibria of short DNA fragments at different ionic strengths, and the intrinsic viscosity of T7 DNA in NaCl solutions. In all cases the theory agrees well with the experiments. The agreement is not convincing for the sedimentation equilibrium at low ionic strength, because here the experimental DNA concentration is too high for the truncated dilute solution expansion of the DNA-salt repulsion.     

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.     

Thermodynamic analysis of the interaction of the xylem water and phloem sugar solution and its significance for the cohesion theory

The cohesion theory explains water transport in trees by the evaporation of water in the leaves (transpiration), which in turn generates the tension required for sap ascent, i.e. the flow of pure water from the soil through the root system and the non-living cells of the tree (xylem tracheids) up to the leaves. Only a small part of this water flow entering the leaves is used in photosynthesis to produce sugar solution, which is transported from the leaves through the living cells (phloem) to everywhere in the tree where it is needed and used. The phloem sieves are connected to the xylem tracheids by water transparent membranes, which means that the upflow of pure water and downflow of sugar solution interact with each other, causing the osmotic pressure in the sugar solution (Münch model). In this paper we analyse this interaction with a thermodynamic approach and we show that some open questions in the cohesion theory can then perhaps be better understood. For example, why under a quite high tension the water can flow in the xylem mostly without any notable cavitation, and how the suction force itself depends on the cavitation. Minimizing Gibbs energy of the system of xylem and phloem, we derive extended vapor pressure and osmotic pressure equations, which include gas bubbles in the xylem conduits as well as the cellulose-air-water interface term. With the aid of the vapor pressure equation derived here, we estimate the suction force that the cavitation controlled by the phloem sugar solution can generate at high moisture contents. We also estimate the suction force that the transpiration can generate by moisture gradient at low moisture contents. From the general osmotic pressure equation we derive an equation for calculating the degree of cavitation with different sugar solution concentrations and we show the conditions under which the cavitation in the xylem is totally avoided. Using recent field measurement results for a Scotch pine, the theory is demonstrated by showing its predictions for possible amounts of cavitation or embolism from morning hours to late afternoon.     

Phospholipid interactions in model membrane systems. II. Theory.

We describe statistical thermodynamic theory for the lateral interactions among phospholipid head groups in monolayers and bilayers. Extensive monolayer experiments show that at low surface densities, PC head groups have strong lateral repulsions which increase considerably with temperature, whereas PE interactions are much weaker and have no significant temperature dependence (see the preceding paper). In previous work, we showed that the second virial coefficients for these interactions can be explained by: (a) steric repulsions among the head groups, and (b) a tilting of the P-N+ dipole of PC so that the N+ end enters the oil phase, to an extent that increases with temperature. It was also predicted that PE interactions should be weaker and less temperature dependent because the N+ terminal of the PE head-group is hydrophilic, hence, it is tilted into the water phase, so dipolar contributions among PE's are negligible due to the high dielectric constant of water. In the present work, we broaden the theory to treat phospholipid interactions up to higher lateral surface densities. We generalize the Hill interfacial virial expansion to account for dipoles and to include the third virial term. We show that to account for the large third virial coefficients for both PC and PE requires that the short range lateral attractions among the head groups also be taken into account. In addition, the third virial coefficient includes fluctuating head group dipoles, computed by Monte Carlo integration assuming pairwise additivity of the instantaneous pair potentials. We find that because the dipole fluctuations are correlated, the average triplet interactions do not equal the sum of the average dipole pair potentials. This is important for predicting, the magnitude and the independence of temperature of the third virial coefficients for PC. The consistency of the theory with data of both the second and the third virial coefficients extends the applicability of the head-group model to semiconcentrated monolayers, in agreement with the surface potential data in the foregoing paper.     

Osmotic pressure of DNA solutions and effective diameter of the double helix

A simple osmometer with nuclear filters (polymer films with pores of a preset diameter) were used to measure the osmotic pressure of Col E1 plasmid DNA solutions in the concentration range of 1-4 mg/ml DNA. Linear and open circular DNA forms proved to have the same osmotic pressure within the experimental accuracy. The results of the measurements were used for calculating the second virial coefficient A2 of the solution of DNA segments and the effective chain diameter d eff in the ionic strength range of 10(-2)-0.1 M. As the ionic strength is lowered from 0.1 to 10(-2) M the effective diameter of DNA increases from 80 to 220 A. The results are in rather good agreement with theory and with other experimental data.     

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.     

Application of a thermodynamic model to the prediction of phase separations in freeze-concentrated formulations for protein lyophilization

Many of the compounds considered for use in pharmaceutical formulations demonstrate incompatibilities with other components at high enough concentrations, including pairs of polymers, polymers and salts, or even proteins in combination with polymers, salts, or other proteins. Freeze concentration can force solutions into a region where incompatibilities between solutes will manifest as the formation of multiple phases. Such phase separation complicates questions of the stability of the formulation as well as labile components, such as proteins. Yet, phase separation events are difficult to identify by common formulation screening methods. In this report, we use the osmotic virial expansion model of Edmond and Ogston (1) to describe phase-separating behavior of ternary aqueous polymer solutions. Second osmotic virial coefficients of polyethylene glycol 3350 (PEG) and dextran T500 were measured by light scattering. Assuming an equilibrium between ice and water in the freeze-concentrated solution, a degree of freeze concentration can be estimated, which, when combined with the phase separation spinodal, describes a "phase separation envelope" in which phase separation tendencies can be expected in the frozen solution. The phase separation envelope is bounded at low temperatures by the glass transition temperature of the freeze-concentrated solution. Scanning electron microscopic images and infrared spectroscopy of protein structure are provided as experimental evidence of the phase separation envelope in a freeze-dried system of PEG, dextran, and hemoglobin.     

Negative second virial coefficients as predictors of protein crystal growth: evidence from sedimentation equilibrium studies that refutes the designation of those light scattering parameters as osmotic virial coefficients

The effects of ammonium sulphate concentration on the osmotic second virial coefficient (BAA/MA) for equine serum albumin (pH 5.6, 20 degrees C) have been examined by sedimentation equilibrium. After an initial steep decrease with increasing ammonium sulphate concentration, BAA/MA assumes an essentially concentration-independent magnitude of 8-9 ml/g. Such behaviour conforms with the statistical-mechanical prediction that a sufficient increase in ionic strength should effectively eliminate the contributions of charge interactions to BAA/MA but have no effect on the covolume contribution (8.4 ml/g for serum albumin). A similar situation is shown to apply to published sedimentation equilibrium data for lysozyme (pH 4.5). Although termed osmotic second virial coefficients and designated as such (B22), the negative values obtained in published light scattering studies of both systems have been described incorrectly because of the concomitant inclusion of the protein-salt contribution to thermodynamic nonideality of the protein. Those negative values are still valid predictors of conditions conducive to crystal growth inasmuch as they do reflect situations in which there is net attraction between protein molecules. However, the source of attraction responsible for the negative virial coefficient stems from the protein-salt rather than the protein-protein contribution, which is necessarily positive.