  Antifreeze proteins (AFPs) are remarkable biomolecules that suppress ice
formation at trace concentrations. To inhibit ice growth, AFPs must not only
bind to ice crystals, but also resist engulfment by ice. The highest
supercooling, $\Delta T^{*}$, for which AFPs are able to resist engulfment is
widely believed to scale as the inverse of the separation, $L$, between bound
AFPs, whereas its dependence on the molecular characteristics of the AFP
remains poorly understood. By using specialized molecular simulations and
interfacial thermodynamics, here we show that in contrast with conventional
wisdom, $\Delta T^{*}$ scales as $L^{-2}$ and not as $L^{-1}$. We further show
that $\Delta T^{*}$ is proportional to AFP size and that diverse naturally
occurring AFPs are optimal at resisting engulfment by ice. By facilitating the
development of AFP structure-function relationships, we hope that our findings
will pave the way for the rational design of novel AFPs.
