Determination of cell membrane permeability coefficients: Comparison of models in the case of oocytes.

Values of cell membranes permeability coefficients for water and molecules of cryoprotective agents (CPAs) are the necessary characteristics for developing physical-mathematical models describing mass transfer processes through cell membranes in order to predict optimal cell cooling rates. We carried out a comparative analysis of the permeability coefficients of mouse oocyte membranes for molecules of water, ethylene glycol (EG), propane-1,2-diol (1,2-PD) and dimethyl sulfoxide (Me2SO), determined by applying the classical Kedem-Katchalsky model, which considers only the penetration of non-electrolyte molecules (water and CPA) through the membrane, and the model developed by us, which takes into account the transmembrane transfer of ions and the associated changes in the transmembrane electric potential. We shown that calculations based on the developed modified model provide lower values of the permeability coefficients of the oocyte membrane for water and CPA molecules. What is important that the obtained by our modified model permeability coefficients for water molecules do not depend on the type of cryoprotectant, while the application of the classical model both in our studies and works of other authors always gave different values of these coefficients in solutions with different cryoprotectants. Our modified model also makes it possible to determine the dynamics of the transmembrane electric potential of the cell under the conditions of transmembrane mass transfer and the duration of the membrane being influenced by the changes in electric potential, that is a parameter that can directly affect the viability of cells.

Physical-mathematical Model of Substance Redistribution between the Cell and its Hypertonic Solution Environment of Penetrating Cryoprotectants with Relevance to Membrane Potential.

BACKGROUND: The redistribution of basic ions between the cell cytoplasm and its surrounding medium due to osmotic action affects transmembrane potential and plasma membrane integrity at all stages of low temperature preservation. OBJECTIVE: To develop a physical-mathematical model describing the redistribution of osmotically active solutes between the cell and its hypertonic solutions of penetrating cryoprotectants that enables the calculation of kinetic changes in cell volume, cryoprotectant and ion concentrations, as well as the cell transmembrane potential during cell equilibration with cryoprotectant solutions. MATERIALS AND METHODS: The study has modeled the mass transfer process of mouse oocytes upon exposure to 1.5 M DMSO and 1,2-Propanediol (1,2-PD) solutions. RESULTS: Equations for changes of the normalized volume as well as intracellular concentrations of DMSO, 1,2-PD, potassium, sodium, chlorine and transmembrane potential have been obtained in a dimensionless form. The membrane permeability coefficients for DMSO and 1,2-propanediol have been determined and compared with the data of Paynter et al (5). CONCLUSION: The study shows that the incorporation of transmembrane ion movement and electrical potential change in the mathematical model leads to lower values of mouse oocyte membrane permeability coefficients for water and cryoprotectants in comparison with data determined by the traditional model.

Theoretical Estimation of the Optimum Cooling Rate of a Cell Suspension at Linear Freezing Modes Based on a Two Factor Theory of Cryodamage.

BACKGROUND: According to the two-factor theory cryodamage arises from intracellular crystallization and solution effects due to freeze concentration. OBJECTIVE: The study aims to evaluate the contribution of two types of cryodamages that are related to extra- and intracellular crystallization. METHODS: The probability of intracellular crystal formation during cooling of cell suspension in cryoprotective solution has been determined based on general thermodynamics theory. RESULTS: According to the obtained correlations and taking into account of the individual characteristics of yeast cells and murine enterocytes, the optimal cooling rates during freezing of these cells in cryoprotectant solutions were determined. CONCLUSION: The proposed algorithm for the estimation of the optimal cooling rates at linear freezing mode of a particular cellular suspension can be utilized to develope methods for cryopreservation of different cell suspensions.