- Zielinski M
- Elliott J
- McGann L

Cryobiology (2013) 67(3) 403-404

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A central requirement in modeling cellular osmotic behaviour is the ability to calculate the chemical potentials of water and of permeating solutes (e.g. cryoprotectants) both inside and outside the cell. The conditions that cells are exposed to during cryopreservation are generally thermodynamically non-ideal. Accordingly, calculations use non-ideal solution theories, such as the multi-solute osmotic virial equation (MSOVE) [J Phys Chem B, 2007;111(7):1775–85]. However, the {MSOVE} requires that the concentrations of all osmotically-contributing solutes in solution be known. While extracellular solutions are generally well-defined, the intracellular composition is typically not known. We have previously shown in practice [Cryobiology, 2008;57(2):130–136], and by way of a thermodynamic proof [Cryobiology, 2011;63(3):318], that when using the {MSOVE} the intracellular solution can be modelled using a “grouped solute” approach, where all non-permeating intracellular solutes are treated as a single “grouped” solute in chemical potential calculations. Although such a grouped solute is a theoretical construct, much like any real solute its thermodynamic parameters, i.e. osmotic virial coefficients, must be known if it is to be included in calculations. A recent publication [Biopreservation and Biobanking, 2012;10(5):462–471] contains the first measurements of grouped solute osmotic virial coefficients for several cell types. The measured coefficients characterise intracellular solution behaviour ranging from ideal to very non-ideal, indicating considerable variation in thermodynamic non-ideality among cell types. Herein we investigate the role of non-ideal intracellular thermodynamics in the theoretical modeling of cellular osmotic equilibrium. Specifically, we have quantified the effect of varying the intracellular grouped solute osmotic virial coefficients on mathematical model predictions of equilibrium cell volume. Theoretical predictions of equilibrium cell volume are directly applicable to models of near-equilibrium slow cooling processes, and, because the driving force for kinetic osmotic transport is determined by a difference in intra- and extracellular chemical potentials, any variations in these equilibrium predictions will also affect the corresponding kinetic models. In this study we calculated equilibrium cell volumes in solutions containing both permeating and non-permeating solutes, using the {MSOVE} to calculate chemical potentials. Predictions were made in solutions of non-permeating solutes with osmolalities ranging from isotonic to 10 times isotonic, as well as in solutions containing concentrations from 0 to 6 molal of the permeating cryoprotectant dimethyl sulphoxide (Me2SO). Intracellular grouped solute second osmotic virial coefficients with values ranging from 0 (ideal) to 8 molal−1 were used to characterize the intracellular solution in the calculations. For the solutions with only non-permeating solutes, the value of the grouped solute osmotic virial coefficient was found to have a minimal effect on predictions: a maximum 10% difference in predicted volume. However, for the solutions containing Me2SO, a more noticeable effect was observed: increasing the assumed grouped solute osmotic virial coefficient (i.e. increasing intracellular non-ideality) resulted in predictions of lower equilibrium cell volumes, ultimately resulting in a maximum 60% difference in predicted volume between the models using the ideal and most non-ideal (8 molal−1) coefficients. These results demonstrate that the thermodynamic properties of the intracellular solution substantially influence model predictions of cellular osmotic behaviour in the presence of permeating solutes. Source of funding: This work was funded by the Canadian Institutes of Health Research (CIHR) {MOP} 86492 and 126778, the Natural Sciences and Engineering Research Council of Canada (NSERC), the University of Alberta, and Alberta Innovates Technology Futures. J.A.W. Elliott holds a Canada Research Chair in Thermodynamics. Conflict of interest: None declared. michalz@ualberta.ca

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