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 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.     

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.     

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.     

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.     

Reflection coefficients of homopore membranes: effect of molecular size and configuration

Osmotic water flow through membranes with uniform defined pores was measured for a variety of macromolecular solutes. Water flow increased linearly with applied hydrostatic pressure, allowing the effective osmotic pressure of the solutes to be estimated by extrapolation. Reflection coefficients for each solute-membrane combination were calculated and correlated with the ratio of solute size to pore size. For the same mean molecular size, proteins were found to have larger reflection coefficients than dextrans. Molecular rigidity may play a role in this difference in behavior.     

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.     

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.     

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.     

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.     

Rapid measurement of protein osmotic second virial coefficients by self-interaction chromatography

Weak protein interactions are often characterized in terms of the osmotic second virial coefficient (B(22)), which has been shown to correlate with protein phase behavior, such as crystallization. Traditional methods for measuring B(22), such as static light scattering, are too expensive in terms of both time and protein to allow extensive exploration of the effects of solution conditions on B(22). In this work we have measured protein interactions using self-interaction chromatography, in which protein is immobilized on chromatographic particles and the retention of the same protein is measured in isocratic elution. The relative retention of the protein reflects the average protein interactions, which we have related to the second virial coefficient via statistical mechanics. We obtain quantitative agreement between virial coefficients measured by self-interaction chromatography and traditional characterization methods for both lysozyme and chymotrypsinogen over a wide range of pH and ionic strengths, yet self-interaction chromatography requires at least an order of magnitude less time and protein than other methods. The method thus holds significant promise for the characterization of protein interactions requiring only commonly available laboratory equipment, little specialized expertise, and relatively small investments of both time and protein.     

Contribution of solvent drag through intercellular junctions to absorption of nutrients by the small intestine of the rat

The lumen of the small intestine in anesthetized rats was recirculated with 50 ml perfusion fluid containing normal salts, 25 mM glucose and low concentrations of hydrophilic solutes ranging in size from creatinine (mol wt 113) to Inulin (mol wt 5500). Ferrocyanide, a nontoxic, quadrupally charged anion was not absorbed; it could therefore be used as an osmotically active solute with reflection coefficient of 1.0 to adjust rates of fluid absorption, Jv, and to measure the coefficient of osmotic flow, Lp. The clearances from the perfusion fluid of all other test solutes were approximately proportional to Jv. From Lp and rates of clearances as a function of Jv and molecular size we estimate (a) the fraction of fluid absorption which passes paracellularly (approx. 50%), (b) coefficients of solvent drag of various solutes within intercellular junctions, (c) the equivalent pore radius of intercellular junctions (50 A) and their cross sectional area per unit path length (4.3 cm per cm length of intestine). Glucose absorption also varied as a function of Jv. From this relationship and the clearances of inert markers we calculate the rate of active transport of glucose, the amount of glucose carried paracellularly by solvent drag or back-diffusion at any given Jv and luminal glucose concentration and the concentration of glucose in the absorbate. The results indicate that solvent drag through paracellular channels is the principal route for intestinal transport of glucose or amino acids at physiological rates of fluid absorption and concentration. In the absence of luminal glucose the rate of fluid absorption and the clearances of all inert hydrophilic solutes were greatly reduced. It is proposed that Na-coupled transport of organic solutes from lumen to intercellular spaces provides the principal osmotic force for fluid absorption and triggers widening of intercellular junctions, thus promoting bulk absorption of nutrients by solvent drag. Further evidence for regulation of channel width is provided in accompanying papers on changes in electrical impedance and ultrastructure of junctions during Na-coupled solute transport.     

A cohesion/tension mechanism explains the gating of water channels (aquaporins) in Chara internodes by high concentration

Isolated internodes of Chara corallina have been used to study the gating of aquaporins (water channels) in the presence of high concentrations of osmotic solutes of different size (molecular weight). Osmolytes were acetone and three glycol ethers: ethylene glycol monomethyl ether (EGMME), diethylene glycol monomethyl ether (DEGMME), and triethylene glycol monoethyl ether (TEGMEE). The 'osmotic efficiency' of osmolytes was quite different. Their reflection coefficients ranged between 0.15 (acetone), 0.59 (EGMME), 0.78 (DEGMME), and 0.80 (TEGMEE). Bulk water permeability (Lp) and diffusive permeabilities (Ps) of heavy water (HDO), hydrogen peroxide (H2O2), acetone, and glycol ethers (EGMME, DEGMME, and TEGMEE) were measured using a cell pressure probe. Cells were treated with different concentrations of osmotic solutes of up to 800 mM ( approximately 2.0 MPa of osmotic pressure). Inhibition of aquaporin activity increased with both increasing concentration and size of solutes (reflection coefficients). As cell Lp decreased, Ps increased, indicating that water and solutes used different passages across the plasma membrane. Similar to earlier findings of an osmotic gating of ion channels, a cohesion/tension model of the gating of water channels in Chara internodes by high concentration is proposed. According to the model, tensions (negative pressures) within water channels affected the open/closed state by changing the free energy between states and favoured a distorted/collapsed rather than the open state. They should have differed depending on the concentration and size of solutes that are more or less excluded from aquaporins. The bigger the solute, the lower was the concentration required to induce a reversible closure of aquaporins, as predicted by the model.     

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.     

Coupling of Solute and Solvent Flows in Porous Lipid Bilayer Membranes

The present experiments were designed to evaluate coupling of water and nonelectrolyte flows in porous lipid bilayer membranes (i.e., in the presence of amphotericin B) in series with unstirred layers. Alterations in solute flux during osmosis, with respect to the flux in the absence of net water flow, could be related to two factors: first, changes in the diffusional component of solute flux referable to variations in solute concentrations at the membrane interfaces produced by osmotic flow through the unstirred layers; and second, coupling of solute and solvent flows within the membrane phase. Osmotic water flow in the same direction as solute flow increased substantially the net fluxes of glycerol and erythritol through the membranes, while osmotic flow in the opposite direction to glycerol flow reduced the net flux of that solute. The observed effects of osmotic water flow on the fluxes of these solutes were in reasonable agreement with predictions based on a model for coupling of solute and solvent flows within the membrane phase, and considerably in excess of the prediction for a diffusion process alone.     

Activity regulation of the betaine transporter BetP of Corynebacterium glutamicum in response to osmotic compensation

As a response to hyperosmotic stress bacterial cells accumulate compatible solutes by synthesis or by uptake. Beside the instant activation of uptake systems after an osmotic upshift, transport systems show also a second, equally important type of regulation. In order to adapt the pool size of compatible solutes in the cytoplasm to the actual extent of osmotic stress, cells down-regulate solute uptake when the initial osmotic stress is compensated. Here we describe the role of the betaine transporter BetP, the major uptake carrier for compatible solutes in Corynebacterium glutamicum, in this adaptation process. For this purpose, betP was expressed in cells (C. glutamicum and Escherichia coli), which lack all known uptake systems for compatible solutes. Betaine uptake mediated by BetP as well as by a truncated form of BetP, which is deregulated in its response to hyperosmotic stress, was dissected into the individual substrate fluxes of unidirectional uptake, unidirectional efflux and net uptake. We determined a strong decrease of unidirectional betaine uptake by BetP in the adaptation phase. The observed decrease in net uptake was thus mainly due to a decrease of Vmax of BetP and not a consequence of the presence of separate efflux system(s). These results indicate that adaptation of BetP to osmotic compensation is different from activation by osmotic stress and also different from previously described adaptation mechanisms in other organisms. Cytoplasmic K+, which was shown to be responsible for activation of BetP upon osmotic stress, as well as a number of other factors was ruled out as triggers for the adaptation process. Our results thus indicate the presence of a second type of signal input in the adaptive regulation of osmoregulated carrier proteins.     

Determination of reflection coefficients of liposomes for some non-electrolytes by osmotic pressure measurement

The reflection coefficients of bilayer lipid vesicles (liposomes) of various compositions have been determined for a number of non-electrolytes. The solutes were the same and the method of measurement was essentially the same as those which have been used to estimate an equivalent pore radius for erythrocytes. The method involves matching the osmotic pressure of solutions of a permeant test solute with that of a known inpermeant solute. Reflection coefficients for cholesterol-containing liposomes and those of erythrocytes are, when account is taken of those solutes known to permeate the erythrocyte by specialized pathways, not greatly different. Lipid bilayers can thus account for most of the permeability characteristics of the cell originally interpreted as due to aqueous pores. Reflection coefficients are significantly higher for egg phosphatidylcholine membranes that contain cholesterol than those which do not. There is a strong correlation between relative permeabilities derived from reflection coefficients and oil-water partition coefficients. There is also good agreement between these permeabilities and permeabilities measured by others, which exhibit an inverse dependence on molecular size. It is suggested that this tendency of membranes to pass small molecules more readily than large molecules, other properties being equal, is a consequence of the surface pressure of the constituent monolayers of the membrane.     

Activity regulation of the betaine transporter BetP of Corynebacterium glutamicum in response to osmotic compensation

As a response to hyperosmotic stress bacterial cells accumulate compatible solutes by synthesis or by uptake. Beside the instant activation of uptake systems after an osmotic upshift, transport systems show also a second, equally important type of regulation. In order to adapt the pool size of compatible solutes in the cytoplasm to the actual extent of osmotic stress, cells down-regulate solute uptake when the initial osmotic stress is compensated. Here we describe the role of the betaine transporter BetP, the major uptake carrier for compatible solutes in Corynebacterium glutamicum, in this adaptation process. For this purpose, betP was expressed in cells (C. glutamicum and Escherichia coli), which lack all known uptake systems for compatible solutes. Betaine uptake mediated by BetP as well as by a truncated form of BetP, which is deregulated in its response to hyperosmotic stress, was dissected into the individual substrate fluxes of unidirectional uptake, unidirectional efflux and net uptake. We determined a strong decrease of unidirectional betaine uptake by BetP in the adaptation phase. The observed decrease in net uptake was thus mainly due to a decrease of V_max of BetP and not a consequence of the presence of separate efflux system(s). These results indicate that adaptation of BetP to osmotic compensation is different from activation by osmotic stress and also different from previously described adaptation mechanisms in other organisms. Cytoplasmic K⁺, which was shown to be responsible for activation of BetP upon osmotic stress, as well as a number of other factors was ruled out as triggers for the adaptation process. Our results thus indicate the presence of a second type of signal input in the adaptive regulation of osmoregulated carrier proteins.     

Solutes in the free space of growing stem tissues

The concentration of osmotically active solutes in the cell wall free space of young stem tissues was studied using a variety of extraction methods. When the intercellular air spaces of etiolated pea (Pisum sativum L.) internodes were perfused with distilled H₂O, the resulting solution contained a solute concentration of about 70 milliosmoles per kilogram. A second procedure involving vacuum infiltration of segments followed by centrifugation to collect the free space solution gave similar results. Apical stem segments yielded free space extracts about twice as concentrated as those from basal portions of the stem. After correcting for dilution of the free space solution by the infiltrated water, the osmotic pressure of the undiluted free space in pea stem tissue was estimated to be 2.9 bars for apical segments, 1.8 bars for basal regions. These values may be somewhat overestimated due to solute efflux from intracellular pools during the extraction procedure. Similar results were obtained for stem regions of etiolated soybean (Glycine max [L.] Merr.) and cucumber (Cucumis sativus L.) seedlings.

From measurements of the electrical conductivity and refractive index of free space extracts before and after ashing, it appears that 25% of the solutes are inorganic electrolytes and 75% are organic nonelectrolytes with an average size similar to that of glucose.

A significant osmotic pressure in the wall space offers an explanation for the frequent observation that nontranspiring plants have negative water potentials. Calculations of hydraulic resistance from water potential data must take into account solutes in the free space, else `apparent,' but unreal, changes in resistance may be calculated.