  Biological antifreezes protect cold-water organisms from freezing. An example
are the antifreeze proteins (AFPs) that attach to the surface of ice crystals
and arrest growth. The mechanism for growth arrest has not been heretofore
understood in a quantitative way. We present a complete theory based on a
kinetic model. We use the `stones on a pillow' picture. Our theory of the
suppression of the freezing point as a function of the concentration of the AFP
is quantitatively accurate. It gives a correct description of the dependence of
the freezing point suppression on the geometry of the protein, and might lead
to advances in design of synthetic AFPs.
