Temperature Dependence of Membrane Permeability Parameters for Five Cell Types Using Nonideal Thermodynamic Assumptions to Mathematically Model Cryopreservation Protocols

Cryopreservation is the process of preserving biological matter at subzero temperatures for long-term storage. During cryopreservation, cells are susceptible to various injuries that can be mitigated by controlling the cooling and warming profiles and cryoprotective agent (CPA) addition and removal procedures. Mathematical modeling of the changing cell volume at different temperatures can greatly reduce the experiments needed to optimize cryopreservation protocols. Such mathematical modeling requires as inputs the cell membrane permeabilities to water and CPA and the osmotically inactive fraction of the cell. Since the intra- and extracellular solutions are generally thermodynamically nonideal, our group has been incorporating the osmotic virial equation to model the solution thermodynamics that underlie the cell volume change equations, adding the second and third osmotic virial coefficients of the grouped intracellular solute to the cell osmotic parameters that must be measured. In our previous work, we reported methods to obtain cell osmotic parameters at room temperature by fitting experimental cell volume kinetic data with equations that incorporated nonideal solution thermodynamics assumptions. Since the relevant cell volume excursions occur at different temperatures, the temperature dependence of the osmotic parameters plays an important role. In this work, we present a new two-part fitting method to obtain five cell-type-specific parameters (water permeability, dimethyl sulfoxide permeability, osmotically inactive fraction, and the second and third osmotic virial coefficients of the intracellular solution) from experimental measurements of equilibrium cell volume and cell volume as a function of time at room temperature and 0 °C for five cell types, namely, human umbilical vein endothelial cells (HUVECs), H9c2 rat myoblasts, porcine corneal endothelial cells (PCECs), the Jurkat T-lymphocyte cell line, and human cerebral microvascular endothelial cells (hCMECs/D3 cell line). The fitting method in this work is based on both equilibrium and kinetic cell volume data, enabling us to solve some technical challenges and expand our previously reported measurement technique to 0 °C. Finally, we use the measured parameters to model the cell volume changes for a HUVEC cryopreservation protocol to demonstrate the impact of the nonideal thermodynamic assumptions on predicting the changing cell volume during freezing and thawing.