Kinetics of osmotic water flow across cell membranes in non-ideal solutions during freezing and thawing

Cryopreservation requires quantitatively analytical models to simulate the biophysical responses of biomaterials during cryopreservation. The Mazur model and other improved ones, such as Karlsson model concerning solutions containing cryoprotectants (CPA), are somehow precluded by some minor points, particularly, the assumption of ideal solutions. To avoid the ideal solution assumption, in this study a new method is developed to simulate water transport across cell membranes in non-ideal solutions during cooling and thawing. The comparison between osmolalities calculated by the linear freezing-point depression used in this new method and other non-ideal ones is conducted and a good agreement is achieved. In addition, in an ideal case, besides a theoretical agreement, this new approach has been validated by its numerical simulation results. Comparisons between this new approach and the traditional ones with an ideal solution assumption have been conducted based on a spherical hypothetical cell. The main results are (1) the predicted non-ideal intracellular water content is larger than the ideal results; (2) the concentration of CPA solutions is directly proportional to the deviation between the non-ideal and ideal curves. In the end, this study presents a direct description of the degree of subcooling of the protoplasm during dynamic cooling. This study demonstrates that our experimental data-based method is a valid one with clear physical interpretations, convenient expressions and a more extensive application room than traditional ones.