Phase diagrams have seen very little use in biology, however they have
been widely appreciated in cryobiology since Cocks and Brower published
an article showing their utility (*Cryobiology***11**: 340-358,
1974). In biological systems, the primary component is water; the entire
system is a collection of compartments filled with an aqueous solution.
As aqueous solutions are cooled, the water forms a crystalline solid
(ice) which has almost no solubility for the solutes that were in the
aqueous solution. As ice forms, then, the solutes will be confined to
the remaining liquid phase, becoming more concentrated. Since this
lowers the freezing point of the aqueous liquid, the system can remain
in equilibrium with a substantial unfrozen fraction. As cooling
continues, the solubility limit of the solution will also be reached,
leading to the precipitation of solutes. These events are succinctly
described by a phase diagram.

Fig. 6.1.1

Starting at the left hand side of the diagram, if the temperature of a solution with 0% salt is lowered, the freezing point occurs at 0ºC. If the solution has salt dissolved in it (i.e. the concentration of salt is below the solubility limit), then the mixture will exist in the brine compartment. As the temperature is lowered, the weight percent of NaCl doesn't change until the thick line is reached. This line defines the freezing point of the solution. Further cooling will take the solution along the curve defined by the thick line until the eutectic point is reaches at -21.2ºC. At this point, the unfrozen compartment of the mixture is saturated with NaCl; any further cooling will cause salt to precipitate out of the mixture.

For freezing biological systems, this left side of the phase diagram is the most important as it describes the osmolality of the solution in which the cells exist. For convenience, this curve can be described by a simple quadratic equation:

The osmolality will follow this curve down to -21.2ºC, where it will hold constant until the temperature is raised once again. Later on we will see how Jim Lovelock applied this phase diagram to cryobiology by explaining the freezing injury suffered by red blood cells, as well as providing an explanation of the cryopreservative effects of such compounds as glycerol and DMSO.

Where *R* is the weight ratio of glycerol:NaCl and C is the total
concentration of solute (g/100g). This equation (and its inverse) will hold as
long as the system is above the eutectic, described by the following
equation:

Where *R* is the weight ratio of glycerol:NaCl and C is the total
concentration of solute. This equation (and its inverse) will hold as
long as the system is above the eutectic, described by the following
equations:

When 0 <= R < 3 then

When 3 <= R < 4 then

When 4 <= R < 18 then

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Document last updated Oct. 21, 1997.

Copyright © 1997, Ken Muldrew.