Theoretical prediction of 'optimal' freezing programmes.

We have developed a quantitative description of the osmotic behaviour of cells during freezing without a presupposed value of the cooling rate. Instead, at all times the intracellular supercooling is maximised provided that it does not exceed a predetermined value 'p' (e.g., 2 degrees C). This should preclude intracellular ice formation, but also ensures that the osmotic gradient and the CPA concentration gradient are limited, as well as the gradient driven transmembrane fluxes of water and CPA. Using the condition of a constant level of supercooling of p degrees C, equations can be derived to generate non-linear cooling curves in which at all times the cooling rate is maximised (to minimise slow cooling damage), while preventing conditions that could lead to fast cooling damage. Simulations of the osmotic events during freezing, and prediction of the 'optimal' freezing curve can be performed provided that values are available for the membrane permeability coefficients for water (L(p)) and cryoprotectant (P(s)), and their respective activation energies, the initial intracellular osmotically active aqueous volume, and the membrane surface area. Simulations are shown, both with and without permeant solute, to demonstrate how the predicted 'optimal' freezing curve is affected by medium composition, and by membrane permeability and osmotic cell characteristics.