A Multisolute Osmotic Virial Equation for Solutions of Interest in Biology

Abstract

The osmotic virial equation was used to predict osmolalities of solutions of interest in biology. The second osmotic virial coefficients, Bi, account for the interactions between identical solute molecules. For multisolute solutions, the second osmotic virial cross coefficient, Bij, describes the interaction between two different solutes. We propose to use as a mixing rule for the cross coefficient the arithmetic average of the second osmotic virial coefficients of the pure species, so that only binary solution measurements are required for multisolute solution predictions. Single-solute data were fit to obtain the osmotic virial coefficients of the pure species. Using those coefficients with the proposed mixing rule, predictions were made of ternary solution osmolality, without any fitting parameters. This method is shown to make reasonably accurate predictions for three very different ternary aqueous solutions: (i) glycerol + dimethyl sulfoxide + water, (ii) hemoglobin + an ideal, dilute solute + water, and (iii) bovine serum albumin + ovalbumin + water.

The effect of solution nonideality on modeling transmembrane water transport and diffusion-limited intracellular ice formation during cryopreservation

“…Finally and importantly, although the semi-empirical model for solution nonideality developed in this study is a major step forward in modeling transmembrane water transport and IIF in complex systems of nonideal solutions, other models such as the virial equation of nonideal solutions developed by Elliott and colleagues [27][28][29] should be investigated. However, this could not be done before all the additional model parameters in the equation for biological cells are available.…”

“…By expressing the chemical potential of both water and solute in terms of the mole fraction of both nonpermeating and permeating solutes, Elliot and co-workers developed a solute transport equation for describing osmotically driven transport across cell membrane in non-dilute solutions. [25][26][27][28][29] Based on the work of Elliot et al, 25,27 Weng et al 23 developed a new set of non-isothermal equations to study the coupled transport of water and permeable CPAs for cells subjected to freezing in nonideal and nondilute solutions. However, all the aforementioned studies were focused on modeling the effect of nonideality on cell dehydration only and its impact on IN and diffusion-limited ICG in cells during freezing has not been explored.…”

Non-ideal Solution Thermodynamics of Cytoplasm

“…While ideal, dilute solution thermodynamics are ubiquitously applied in biology, the application of ideal dilute solution behavior to concentrated solutions, such as those that occur during cryopreservation or desiccation, will introduce errors-sometimes severe, and may be misleading even in physiological conditions such as for the complex solution containing macromolecules that contributes to the cytoplasm. 3 The relationship between osmolality and concentration is well described for a variety of solutions, including the cytoplasm of erythrocytes. 3,4 However, other than the simplest proposition of osmolality depending linearly on concentration, this relationship has not been available for the cytoplasm of a nucleated mammalian cell.…”

“…3 The relationship between osmolality and concentration is well described for a variety of solutions, including the cytoplasm of erythrocytes. 3,4 However, other than the simplest proposition of osmolality depending linearly on concentration, this relationship has not been available for the cytoplasm of a nucleated mammalian cell.…”

“…Herein, we use the osmotic virial equation, a non-ideal solution thermodynamics model, being applied with success in cryobiological modeling of the extracellular solution. [23][24][25][26][27][28][29] While the solution properties are known for some individual components (e.g., hemoglobin 3,30 ) and combinations of known single-solute components using, for example, the osmotic virial equation, 3,26 the cytoplasm is too complex to make general use of the individual solute solution properties feasible. It is precisely because of the requirement to incorporate thermodynamics of a wide variety of molecules that we have chosen the osmotic virial approach.…”