**2.4 Osmotic flows in cryopreserving mammalian embryos**

#### **2.4.1 Slow-cooling**

In a general slow-cooling procedure, embryos are immersed into permeating cryoprotectants. Intracellular water leaves the cells by osmosis and re-enters the cells together with the permeating cryoprotectants by diffusion. A temporal osmotic equilibrium state is acquired at the end. A 1-2M permeating cryoprotecting agent(s) is often used in slow-cooling. To cryopreserve the embryos, embryos and the surrounding freezing medium are loaded into a plastic straw and subjected to cooling to a temperature slightly lower than the freezing point, i.e. at about -7°C. Controlled ice nucleation is initiated by touching the straw with a cooler surface (e.g., a pair of forceps) to initiate the growth of ice inside the straw. The embryos themselves remain unfrozen but supercooled. The removal of water from the solution by the growing ice crystals increases the solute concentration of the extracellular medium. By osmosis, the intercellular water leaves the cells, resulting in an increase of cryoprotectant concentration in the cells. The subsequent slow cooling further dehydrates the embryos and concentrates the cryoprotectant in the cells to promote intracellular solidification, without intracellular ice formation, at a sufficiently low temperature. If the cooling is too fast, it leads to intracellular ice formation because the intracellular solute has not yet achieved a sufficiently high concentration. Too slow a cooling rate causes cells' death due to the prolonged exposure to hypertonic conditions. The cooling rate must be carefully controlled for each embryonic stage of each species because the permeability of cell membranes, and thus the hydrodynamics, of different samples, can be different.

#### **2.4.2 Vitrification**

In cryopreservation by vitrification (or rapid-cooling), equilibration of cryoprotectants in the embryos and the cryoprotecting medium are not required. Embryos are first permeated by cryoprotecting agents at a low concentration and then immersed in a moderately high concentration (4M or above) of the same cryoprotecting agent, sometimes together with non-permeating cryoprotectants such as 0.5M sucrose. In the presence of the nonpermeating cryoprotectants, the embryos shrink osmotically, thus further increasing concentration of intracellular cryoprotectants. The high concentration of cryoprotecting agents in the medium prevents efflux of intracellular cryoprotecting agents by diffusion (Figure 4). The embryos are then loaded into a container and are rapidly cooled to solidify the embryos without the formation of ice crystals (Rall, 1987). Mathematical modelings such as the relativistic permeability approach is able to simulate the osmotic curve in these

embryos. When the mouse morulae were stored in 1.5M ethylene glycol or glycerol for 6 hours, the majority (>75%) of the embryos retained the capacity to develop into expanded blastocysts (Kasai et al., 1981). To minimize the toxic effect of the cryoprotecting solution to the embryos while retaining the cryoprotecting function, a mixture of two or more cryoprotecting agents could be used to decrease the relative concentration of each chemical. Macromolecules such as polyethylene glycol, ficoll and polyvinylpyrrolidone, which increase the viscosity of a solution, thus slowing down water molecules associating to form ice crystals when cooling, can also lower the concentration of cryoprotecting agents to be

In a general slow-cooling procedure, embryos are immersed into permeating cryoprotectants. Intracellular water leaves the cells by osmosis and re-enters the cells together with the permeating cryoprotectants by diffusion. A temporal osmotic equilibrium state is acquired at the end. A 1-2M permeating cryoprotecting agent(s) is often used in slow-cooling. To cryopreserve the embryos, embryos and the surrounding freezing medium are loaded into a plastic straw and subjected to cooling to a temperature slightly lower than the freezing point, i.e. at about -7°C. Controlled ice nucleation is initiated by touching the straw with a cooler surface (e.g., a pair of forceps) to initiate the growth of ice inside the straw. The embryos themselves remain unfrozen but supercooled. The removal of water from the solution by the growing ice crystals increases the solute concentration of the extracellular medium. By osmosis, the intercellular water leaves the cells, resulting in an increase of cryoprotectant concentration in the cells. The subsequent slow cooling further dehydrates the embryos and concentrates the cryoprotectant in the cells to promote intracellular solidification, without intracellular ice formation, at a sufficiently low temperature. If the cooling is too fast, it leads to intracellular ice formation because the intracellular solute has not yet achieved a sufficiently high concentration. Too slow a cooling rate causes cells' death due to the prolonged exposure to hypertonic conditions. The cooling rate must be carefully controlled for each embryonic stage of each species because the permeability of cell

membranes, and thus the hydrodynamics, of different samples, can be different.

In cryopreservation by vitrification (or rapid-cooling), equilibration of cryoprotectants in the embryos and the cryoprotecting medium are not required. Embryos are first permeated by cryoprotecting agents at a low concentration and then immersed in a moderately high concentration (4M or above) of the same cryoprotecting agent, sometimes together with non-permeating cryoprotectants such as 0.5M sucrose. In the presence of the nonpermeating cryoprotectants, the embryos shrink osmotically, thus further increasing concentration of intracellular cryoprotectants. The high concentration of cryoprotecting agents in the medium prevents efflux of intracellular cryoprotecting agents by diffusion (Figure 4). The embryos are then loaded into a container and are rapidly cooled to solidify the embryos without the formation of ice crystals (Rall, 1987). Mathematical modelings such as the relativistic permeability approach is able to simulate the osmotic curve in these

**2.4 Osmotic flows in cryopreserving mammalian embryos** 

used in vitrification.

**2.4.1 Slow-cooling** 

**2.4.2 Vitrification** 

processes to facilitate the optimization of vitrification protocols in future (Katkov and Pogorelov, 2007).
