Ronald L. Levin

Water permeability of yeast cells at sub-zero temperatures.

SummaryA combined cryomicroscopic-multiple nonlinear regression analysis technique has been used to determine the water permeability of the yeast cellSaccharomyces cerevisiae during freezing. The time rate of change in volume of “supercooled” yeast cells was photographically monitored using a “cryomicroscope” which is capable of controlling in a programmable manner both the temperature and the time rate of change in temperature of the cell suspension being studied. Multiple nonlinear regression analysis together with a thermodynamic model of cell water transport during freezing was then used to statistically deduce the subzero temperature dependence of the cell water permeability. The water permeability process forS. cerevisiae being cooled at subzero temperatures was found to be rate-limited by the passage of water through either the plasmalemma, the cell wall, or a combination of these two permeability barriers. The hydraulic water permeability coefficient for yeast at 20°C is approximately 1–2×10−13 cm3/dyne sec, if extrapolation from subzero temperatures to room temperature is permissible, while the apparent activation energy governing the permeability process at subzero temperatures is approximately 45–68 kJ/mol (11–16 kcal/mol).

An optimum method for the introduction or removal of permeable cryoprotectants: isolated cells.

Abstract On the basis of a nonequilibrium model for the transport of water and permeable solute across cell membranes, an optimum method has been devised for the introduction and the removal of a permeable cryoprotectant from single, isolated cells so that potentially lethal drastic alterations in cellular volume are minimized. The method involves the simultaneous variation of both the permeable (an initial step change, followed by a linear variation with time which overshoots the terminal value, and a final step change to the terminal value) and impermeable (an initial step change in the opposite direction of the permeable solute concentration change, followed by a period where the concentration remains constant, and a final step change back to the initial value) extracellular solute concentrations in a prescribed manner such that both the cellular water content and the intracellular electrolyte concentration remain constant as the intracellular permeable solute (CPA) concentration is either raised or lowered. The results of our theoretical analysis indicate that the osmotic stresses and strains usually imposed upon cells during the introduction and the removal of permeable cryoprotectants can be minimized and that the resulting protocols are clinically the most efficient.

Cryomicroscopy of isolated plant protoplasts

Abstract It has been nearly 100 years since Muller-Thurgau (26) employed cryomicroscopy to identify the cooling rate dependency of intracellular ice formation. Since that time cryomicroscopy has advanced from the “ice age” when Molisch (23) packed his microscope in ice to the “space age” of today when computer hardware developed for space satellite imagery is used for cryomicroscopic image analysis. Although interest in cryomicroscopy has been sporadic in the intervening period, current interest is at a high level—largely as a result of the refinement in the cryomicroscope design by Diller and Cravalho (9). The increased sophistication in cryostage design and precision of temperature control allow for quantitative studies of cell behavior during a freeze-thaw cycle. Not only does quantitative video image analysis facilitate this task, but it provides for increased resolution of cellular and subcellular responses during the freeze-thaw cycle. Most importantly, cryomicroscopy presents a researcher with a panorama of cellular behavior within which existing facts can be placed in perspective and from which future experiments can be more accurately focused.

The freezing of finite domain aqueous solutions: Solute redistribution

Abstract An analysis of the unidirectional freezing of finite domain aqueous solutions during cooling at subzero temperatures is presented. Under conditions where the solute is completely rejected by the advancing ice front, the conventional diffusion equation is invalid and suitable transport expressions can only be obtained by an appropriate variable transformation from the laboratory frame of reference where the volume of the liquid region varies with time to a “solute-fixed” frame of reference where the volume of the liquid region remains constant (Levin et al. [34]). Such an analysis results in a nonlinear parabolic partial differential diffusion equation in the laboratory frame with a spatially and time varying effective convective velocity term in addition to the usual time and spatial derivative terms. The analysis is valid at both short and long times and also for both ideal, dilute and non-ideal, non-dilute solutions. Additional approximations are made only to the extent that the liquid-solid interface is assumed to remain planar and that the system is assumed to remain in thermal equilibrium during the freezing process. Generalized results are obtained for initially ideal, dilute aqueous solutions cooled at various rates on one boundary by standard numerical methods. These results indicate that non-uniform concentration profiles can exist within the liquid region of systems during freezing and that the variation with time/temperature of the volumes of the liquid and solid regions is significantly affected by the non-uniform distribution of solutes. Our results also indicate that under certain circumstances (e.g. fast cooling rates) that the solidification process may be limited by mass transfer considerations, that is, by the ability of the solutes to diffuse away from the interface, rather than solely by the heat-transfer considerations of whether or not the sensible and latent heats can be removed.

Generalized analytical solution for the freezing of a supercooled aqueous solution in a finite domain

Abstract A generalized analytical solution to the problem of the unidirectional planar freezing at a constant temperature of a supercooled aqueous solution of finite extent is presented. This solution is valid for both dilute and non-dilute solutions and also at both short and long times. Mathematical approximations are made only to the extent that the mass diffusivity is considered to be independent of concentration. Our theoretical results compare favorably with the experimental results of other investigators and demonstrate that transient non-uniform concentration profiles can exist within the liquid region of systems as freezing progresses and that the volumes of the liquid and solid regions can vary non-linearly with time. The extent of concentration polarization and the velocity of propagation of the liquid-solid interface are found to be functions of the initial degree of supercooling, the mass diffusivity, and the initial size of the system. A comparison is also made between our results for freezing in finite domains and the classical similarity results for freezing in semi-infinite domains.