Insights into the model of non-perfect osmometer cells for cryopreservation: a parametric sweep analysis

Recently, a mathematical model able to describe the non-perfect osmotic behavior of cells during cryopreservation was proposed. The model improves the two-parameter formalism typically adopted in cryopreservation literature by allowing the transmembrane permeation of ions/salt, through the temporary opening of mechanosensitive channels whenever membrane stretching occurs: cells can reach an equilibrium volume different from the initial one, when isotonic conditions are re-established after contacting with impermeant or permeant solutes, such as sucrose or a cryoprotectant agent like dimethyl sulfoxide, respectively. Although the model was conceived as a conservative development of the two-parameter formalism to avoid over-parameterization, a complex picture of the system emerges. To describe this, first an appropriate non-dimensional version of the model equations is derived. Then, a parametric sweep analysis is performed and discussed to highlight the features of the novel model in comparison with the two-parameter formalism: the conditions by which the first reduces to the second are identified. Only equilibrium equations with impermeant sucrose may be analytically derived from the model: their validity is here extended much more than originally assumed. When permeant dimethyl sulfoxide comes into play, the temporary opening of mechanosensitive channels is difficult to predict and prevents the derivation of the equilibrium equations: in this case, a numerical integration of system dynamics up to steady state is required to determine the cell volume at equilibrium. In conclusion, cell volume at equilibrium depends on the position of the temporal window of mechanosensitive channels opening, which, in general, is a complex function of model parameters and operating conditions. (Graphical abstract: https://ars.els-cdn.com/content/image/1-s2.0-S001122402030657X-fx1_lrg.jpg)