Permeability and Osmotic Parameters of Human Umbilical Vein Endothelial Cells and H9C2 Cells under Non-ideal Thermodynamic Assumptions: A Novel Iterative Fitting Method

Use of membrane transport models to design cryopreservation procedures for oocytes

Oocyte cryopreservation is increasingly being used in reproductive technologies for conservation and breeding purposes. Further development of oocyte cryopreservation techniques requires interdisciplinary insights in the underlying principles of cryopreservation. This review aims to serve this purpose by: (1) highlighting that preservation strategies can be rationally designed, (2) presenting mechanistic insights in volume and osmotic stress responses associated with CPA loading strategies and cooling, and (3) giving a comprehensive listing of oocyte specific biophysical membrane characteristics and commonly used permeation model equations. It is shown how transport models can be used to simulate the behavior of oocytes during cryopreservation processing steps, i.e., during loading of cryoprotective agents (CPAs), cooling with freezing as well as vitrification, warming and CPA unloading. More specifically, using defined cellular and membrane characteristics, the responses of oocytes during CPA (un)loading were simulated in terms of temperature- and CPA type-and-concentration-dependent changes in cell volume and intracellular solute concentration. In addition, in order to determine the optimal cooling rate for slow programmable cooling cryopreservation, the freezing-induced cell volume response was simulated at various cooling rates to estimate rates with tolerable limits. For vitrification, special emphasis was on prediction of the timing of reaching osmotic tolerance limits during CPA exposure, and the need to use step-wise CPA addition/removal protocols. In conclusion, we present simulations and schematic illustrations that explain the timing of events during slow cooling cryopreservation as well as vitrification, important for rationally designing protocols taking into account how different CPA types, concentrations and temperatures affect the oocyte.

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.

Predicting freezing points of ternary salt solutions with the multisolute osmotic virial equation

Previously, the multisolute osmotic virial equation with the combining rules of Elliott et al. has been shown to make accurate predictions for multisolute solutions with only single-solute osmotic virial coefficients as inputs. The original combining rules take the form of an arithmetic average for the second-order mixed coefficients and a geometric average for the third-order mixed coefficients. Recently, we derived generalized combining rules from a first principles solution theory, where all mixed coefficients could be expressed as arithmetic averages of suitable binary coefficients. In this work, we empirically extended the new model to account for electrolyte effects, including solute dissociation, and demonstrated its usefulness for calculating the properties of multielectrolyte solutions. First, the osmotic virial coefficients of 31 common salts in water were tabulated based on the available freezing point depression (FPD) data. This was achieved by polynomial fitting, where the degree of the polynomial was determined using a special criterion that accounts for the confidence intervals of the coefficients. Then, the multisolute model was used to predict the FPD of 11 ternary electrolyte solutions. Furthermore, models with the new combining rules and the original combining rules of Elliott et al. were compared using both mole fraction and molality as concentration units. We find that the mole-fraction-based model with the new combining rules performs the best and that the results agree well with independent experimental measurements with an all-system root-mean-square error of 0.24 osmoles/kg (0.45 °C) and close to zero mean bias for the entire dataset (371 data points).

Permeation kinetics of dimethyl sulfoxide in porcine corneoscleral discs

The cornea is the transparent tissue in front of the eye that bends light to help the eye focus. More than five million people's vision can be restored by a corneal transplant (keratoplasty), but there is a scarcity of suitable donor tissue. Cryopreservation could potentially increase the on-demand availability of corneas by reducing expiration and contamination during hypothermic storage, and allow equitable distribution. Understanding the transport of water and cryoprotectants across the tissue is important in developing effective cryopreservation protocols. Here, we first measured the shrinking and swelling kinetics at 22 °C and 0 °C of porcine corneoscleral discs when exposed to phosphate-buffered saline and to a cryoprotectant vehicle solution containing 2.5% chondroitin sulfate and 1% dextran. Other valuable measurements were made including the density and osmolality of the vehicle solution at 0 °C, and the water fraction of porcine cornea and sclera. Using the knowledge gained from this first part to minimize background swelling, we then examined permeation kinetics of dimethyl sulfoxide (Me2SO) in porcine corneoscleral discs at 0 °C, the temperature at which cryoprotectant loading typically occurs. The concentration data obtained as a function of time were fitted to a Fick's law model of one-dimensional diffusion to measure an effective diffusion coefficient of Me2SO, which was found to be 5.306×10-11 m2/s. We further quantified permeation kinetics of Me2SO in sclera alone at 0 °C to support our hypothesis that our measurements for corneoscleral discs will not be affected by the presence of the sclera. The obtained effective diffusion coefficient can be used in modelling aimed at developing cryopreservation protocols that minimize the exposure time of the corneas during the cryoprotectant loading step.

Comparison of dilute and nondilute osmotic equilibrium models for erythrocytes

Successful cryopreservation requires the addition of cryoprotective agents (CPAs). The addition of permeating CPAs, such as glycerol, is associated with some risk to the cells and tissues. These risks are both related to the CPA themselves (CPA toxicity) and to the volume response of the cell (osmotic damage). To minimize the potential for damage during cryopreservation, mathematical models are often employed to understand the interactions between protocols and cell volume responses. In the literature, this volume response is usually captured using ideal and dilute approximations of chemical potential and osmolality, an approach that has been called into question for cells in high concentrations of CPAs. To address this, the relevance of non-ideal and non-dilute models has been explored in a number of cell types in the presence of permeating CPAs. However, it has not been explored in erythrocytes, which have a cytosolic hemoglobin content of more than 20% by volume and are cryopreserved in 40% glycerol. Because hemoglobin has been suggested to be a highly non-ideal solute, if the non-ideal and non-dilute transport model is relevant to any cells, it should be relevant to erythrocytes. Here we investigate the use, and accuracy, of both the dilute and non-dilute models in predicting cell volume changes during CPA equilibration in erythrocytes, and demonstrate that using published values for the non-ideal and non-dilute model, applied to erythrocytes, leads to model predictions inconsistent with experimental data, whereas dilute approximations align well with experimental data.