Continuous measurement of protein osmotic pressure in blood and lymph of sheep

We have continuously measured protein osmotic pressure of blood and lymph in sheep to compare two kinds of needle osmometers (rigid and flexible) with a membrane osmometer (Wescor). We also compared the averaged values of the continuous measurement with osmotic pressure calculated from total protein and albumin fraction, using the Yamada equation. The rigid-needle and membrane osmometers showed excellent correlation (y = 1.00x + 0.06; r greater than 0.99). The flexible-needle osmometer tended to overestimate osmotic pressure (avg 16%). We used the rigid-needle osmometer for continuous measurements of protein osmotic pressure of blood and lymph in anesthetized or unanesthetized sheep to observe changes in protein osmotic pressure of blood and lymph through the three different interventions. The relationship between the theoretical values (x) and the continuous measurements (y) of osmotic pressure was good (y = 0.99x + 0.16, r = 0.97), but after various interventions, the continuously measured protein osmotic pressure tended to exceed the calculated measurements. The continuous measurement should be monitored with spot samples measured in a stationary osmometer or by calculation of osmotic pressure from total protein concentration and albumin fraction.     

Plasma protein osmotic pressure equations and nomogram for sheep

The equations developed by Landis and Pappenheimer (Handbook of Physiology. Circulation, 1963, p. 961-1034) for calculating the protein osmotic pressure of human plasma proteins have been frequently used for other animal species without regard to the fractional albumin concentration or correction for protein-protein interaction. Using an electronic osmometer, we remeasured the protein osmotic pressure of purified sheep albumin and sheep plasma partially depleted of albumin. We measured protein osmotic pressures of serial dilutions over the concentration range 0-180 g/l for albumin and 0-100 g/l for the albumin-depleted proteins at room temperature (26 degrees C). Using a nonlinear least squares parameter-fitting computer program, we obtained the equation of best fit for purified albumin, and then we used that equation together with the measured albumin fraction to obtain the best-fit equation for the nonalbumin proteins. The equation for albumin is IIcmH2O,39 degrees C = 0.382C + 0.0028C2 + 0.000013C3, where C is albumin concentration in g/l. The equation for the nonalbumin fraction is IIcmH2O,39 degrees C = 0.119C + 0.0016C2. Up to 200- and 100-g/l protein concentration, respectively, these equations give the least standard error of the estimate for each of the virial coefficients. The computed number-average molecular weight for the nonalbumin proteins is 222,000. Using the new equations, we constructed a nomogram, based on the one of Nitta and co-workers (Tohoku J. Exp. Med. 135: 43-49, 1981). We tested the nomogram using 144 random samples of sheep plasma and lymph from 31 sheep. We obtained a correlation coefficient of 0.99 between the measured and nomogram estimates of protein osmotic pressure.     

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.     

Effective hard particle model for the osmotic pressure of highly concentrated binary protein solutions

The experimentally measured concentration dependence of the osmotic pressure of an equimolar mixture of hen egg ovalbumin and bovine serum albumin at pH 7.0 and 25°C in the presence of 0.15 M NaCl is shown to be quantitatively accounted for by a model in which each protein species is represented by an effective hard sphere. The size of this sphere is determined by analysis of the concentration dependence of the osmotic pressure of the isolated protein.     

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.     

Evaluation of the water potentials of solutions of polyethylene glycol 8000 both in the absence and presence of other solutes

Published and additional data for polyethylene glycol 8000 (PEG), formerly PEG 6000, solution water potentials (Ψ) are compared. Actual bars Ψ over the concentration range of 0 to 0.8 gram PEG per gram H₂O and temperature (T) range of 5 to 40°C are best predicted (probably within ± 5%) by this equation: Ψ = 1.29[PEG]²T − 140[PEG]² − 4.0[PEG]. Although transformable through division by [PEG] to virial equation form, results indicate that the coefficients are not virial. Mannitol (MAN) interacts with PEG to produce Ψ significantly lower than additive. Vapor pressure osmometer (VPO) data for MAN-PEG synergism compared favorably with those from thermocouple hygrometry; and VPO data showing the interactions between PEG and four salts are presented. The synergism of MAN-PEG and of NaCl-PEG are related linearly to the concentration of solute added with PEG.     

Osmotic Pressure of DNA Solutions and Effective Diameter of the Double Helix

Abstract

A simple osmometer with nuclear filters (polymer films with pores of a preset diameter) were used to measure the osmotic pressure of Col El 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 A ₂ 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.     

The origin and consequences of concentration dependence in gel chromatography

Concentration dependence of elution volume was determined for Blue Dextran 2000, Dextran 500, Dextran sulphate 500 and bovine serum albumin on columns of Sephadex G-100 equilibrated with sodium phosphate buffer, I 0.1, pH6.8. From the results for Dextran 500, it was shown that a linear relation exists between elution volume and the corresponding osmotic pressure calculated for the same concentration and incorporating the term containing the second virial coefficient. This relationship was used to predict the concentration dependence of elution volume for bovine serum albumin and myoglobin, proteins that partially penetrate Sephadex G-100. Possible consequences of osmotic effects are considered in relation to various types of column experiments, including differential chromatography.     

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.     

Application of polyelectrolyte limiting laws to virial and asymptotic expansions for the Donnan equilibrium

We have applied a general polyelectrolyte theory to an analysis of the Donnan equilibrium. The polyelectrolyte concentration is measured by a dimensionless parameter x, equal to the ratio of the equivalent polyelectrolyte concentration to the concentration of salt in the external compartment. For small x, virial series - expansions in powers of x - are developed for the Donnan salt-exclusion, osmotic pressure, and electromotive force. For large x, asymptotic expansions for these effects are presented. Polyion-polyion interactions are explicitly neglected, so that the physical significance of the virial series differs from its meaning in neutral polymer chemistry. Numerical results illustrate large deviations from ideal Donnan behavior as well as satisfactory agreement with published data on the salt-exclusion and emf effects. However, results for the Donnan osmotic pressure disagree with the data, except in the case of zero salt concentration in the external compartment, for which agreement is almost exact.     

Determination of the second virial coefficient of bovine serum albumin under varying pH and ionic strength by composition-gradient multi-angle static light scattering

Composition-gradient multi-angle static light scattering (CG-MALS) is an emerging technique for the determination of intermolecular interactions via the second virial coefficient B₂₂. With CG-MALS, detailed studies of the second virial coefficient can be carried out more accurately and effectively than with traditional methods. In addition, automated mixing, delivery and measurement enable high speed, continuous, fluctuation-free sample delivery and accurate results. Using CG-MALS we measure the second virial coefficient of bovine serum albumin (BSA) in aqueous solutions at various values of pH and ionic strength of a univalent salt (NaCl). The systematic variation of the second virial coefficient as a function of pH and NaCl strength reveals the net charge change and the isoelectric point of BSA under different solution conditions. The magnitude of the second virial coefficient decreases to 1.13 x 10⁻⁵ ml*mol/g² near the isoelectric point of pH 4.6 and 25 mM NaCl. These results illuminate the role of fundamental long-range electrostatic and van der Waals forces in protein-protein interactions, specifically their dependence on pH and ionic strength. Electronic supplementary material The online version of this article (doi:10.1007/s10867-014-9367-7) contains supplementary material, which is available to authorized users.     

OSMOTIC PROPERTIES OF THE EGG CELLS OF THE OYSTER (OSTREA VIRGINICA)

Investigations of the osmotic properties of oyster eggs by a diffraction method for measuring volumes have led to the following conclusions: 1. The product of cell volume and osmotic pressure is approximately constant, if allowance is made for osmotically inactive cell contents (law of Boyle-van''t Hoff). The space occupied by osmotically inactive averages 44 per cent of cell volume. 2. Volume changes over a wide range of pressures are reversible, indicating that the semipermeability of the cell during such changes remains intact. 3. The kinetics of endosmosis and of exosmosis are described by the equation, See PDF for Equation, where dV is rate of volume change; S, surface area of cell, (P-P_e), the difference in osmotic pressure between cell interior and medium, and K, the permeability of the cell to water. 4. Permeability to water during endosmosis is 0.6µ³ of water per minute, per square micron of cell surface, per atmosphere of pressure. The value of permeability for exosmosis is closely the same; in this respect the egg cell of the oyster appears to be a more perfect osmometer than the other marine cells which have been studied. Permeability to water computed by the equation given above is in good agreement with computations by the entirely different method devised by Jacobs. 5. Permeability to diethylene glycol averages 27.2, and to glycerol 20.7. These values express the number of mols x 10^–15 which enter per minute through each square micron of cell surface at a concentration difference of 1 mol per liter and a temperature of 22.5°C. 6. Values for permeability to water and to the solutes tested are considerably higher for the oyster egg than for other forms of marine eggs previously examined. 7. The oyster egg because of its high degree of permeability is a natural osmometer particularly suitable for the study of the less readily penetrating solutes.     

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.     

Osmotic pressure method to measure salt induced folding/unfolding of bovine serum albumin

A new approach has been developed to monitor protein folding by utilizing osmotic pressure and a range of salt concentrations in a well characterized protein, bovine serum albumin (BSA). It is hypothesized that both the ‘effective’ osmotic molecular weight, A_e, and the solute/solvent interaction parameter, I, in the empirical relation $\text{M}{}_{\mathrm{solvent}}\text{M}{}_{\mathrm{solute}}\text{= (}\text{RTϱ}\text{A}{}_{\mathrm{e}}\text{)}\text{1}\text{gp}\text{+ I}$ [1] can be used as measures of protein folding. I is a measure of solvent perturbed by the solute and is thought to depend directly upon the solvent accessible surface area (ASA). It is reasoned that larger solvent accessible surface area of an unfolded or denatured protein should perturb more water and produce larger I-values. Thus I-values allow calculation of a unfolded protein fraction, f_u^a, due to changes in relative solvent accessible surface area. It has been observed that A_e decreases for filamentous, denatured proteins due to segmental motion of the molecule [2]. This allows calculation of unfolded protein fraction from the effective molecular weight, f_u^m. Colloid osmotic pressure of BSA was measured in a range of salt concentrations at 25°C, and pH = 7 (above the isoelectric point of BSA at pH = 5.4). Both S and I were used to monitor protein folding as the salt concentration was varied. In general, larger and variable I-values and smaller A_e were observed at salt concentrations less than 50 mmolal NaCl (I_max = 8.9), while constant I = 4.1 and A_e = 66,500 were observed above 50 mmolal NaCl. The two expressions for fractional unfolding (f_u^a and f_u^m) are in general agreement. Small differences in the parameters below 50 mmolal salt concentration are explained with well known shifts in the relative amounts of α-helix, β-sheet and random coil in denatured BSA. The relative amounts of these shifts agree with predictions in the literature attributed to continuous BSA expansion rather than an ‘all-or-none’ conversion.     

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.     

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.     

Direct measurement of protein osmotic second virial cross coefficients by cross-interaction chromatography

The importance of weak protein interactions, such as protein self-association, is widely recognized in a variety of biological and technological processes. Although protein self-association has been studied extensively, much less attention has been devoted to weak protein cross-association, mainly due to the difficulties in measuring weak interactions between different proteins in solution. Here a framework is presented for quantifying the osmotic second virial cross coefficient directly using a modified form of self-interaction chromatography called cross-interaction chromatography. A theoretical relationship is developed between the virial cross coefficient and the chromatographic retention using statistical mechanics. Measurements of bovine serum albumin (BSA)/lysozyme cross-association using cross-interaction chromatography agree well with the few osmometry measurements available in the literature. Lysozyme/alpha-chymotrypsinogen interactions were also measured over a wide range of solution conditions, and some counterintuitive trends were observed that may provide new insight into the molecular origins of weak protein interactions. The virial cross coefficients presented in this work may also provide insight into separation processes that are influenced by protein cross-interactions, such as crystallization, precipitation, and ultrafiltration.     

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.     

Measurement of osmotic second virial coefficients by zonal size-exclusion chromatography

Numerical simulation of protein migration reflecting linear concentration dependence of the partition isotherm has been used to invalidate a published procedure for measuring osmotic second virial coefficients (B₂₂) by zonal exclusion chromatography. Failure of the zonal procedure to emulate its frontal chromatographic counterpart reflects ambiguity about the solute concentration that should be used to replace the applied concentration in the rigorous quantitative expression for frontal migration; the recommended use of the peak concentration in the eluted zone is incorrect on theoretical grounds. Furthermore, the claim for its validation on empirical grounds has been traced to the use of inappropriate B₂₂ magnitudes as the standards against which the experimentally derived values were being tested.     

Predicting the Activity Coefficients of Free-Solvent for Concentrated Globular Protein Solutions Using Independently Determined Physical Parameters

The activity coefficient is largely considered an empirical parameter that was traditionally introduced to correct the non-ideality observed in thermodynamic systems such as osmotic pressure. Here, the activity coefficient of free-solvent is related to physically realistic parameters and a mathematical expression is developed to directly predict the activity coefficients of free-solvent, for aqueous protein solutions up to near-saturation concentrations. The model is based on the free-solvent model, which has previously been shown to provide excellent prediction of the osmotic pressure of concentrated and crowded globular proteins in aqueous solutions up to near-saturation concentrations. Thus, this model uses only the independently determined, physically realizable quantities: mole fraction, solvent accessible surface area, and ion binding, in its prediction. Predictions are presented for the activity coefficients of free-solvent for near-saturated protein solutions containing either bovine serum albumin or hemoglobin. As a verification step, the predictability of the model for the activity coefficient of sucrose solutions was evaluated. The predicted activity coefficients of free-solvent are compared to the calculated activity coefficients of free-solvent based on osmotic pressure data. It is observed that the predicted activity coefficients are increasingly dependent on the solute-solvent parameters as the protein concentration increases to near-saturation concentrations.