(22e) Antifreeze Proteins: From Interfacial Thermodynamics and Engulfment Resistance to Thermal Hysteresis Predictions

Biological anti-freeze proteins (AFPs) protect organisms at freezing conditions by attaching to the ice surface and arresting its growth. In the theory of DeVries et al., each adsorbed AFP locally pins the ice surface, resulting in a metastable dimple for which the interfacial forces counteract the driving force for growth. As supercooling increases, these metastable dimples become deeper until metastability is lost in an “engulfment” event where the ice irreversibly swallows the AFP. The supercooled temperature below which AFPs can no longer prevent the growth of ice defines the thermal hysteresis (TH). Engulfment resembles nucleation in some respects, and this paper develops a model for the “critical profile” and free energy barrier for the engulfment process. Specifically, we develop a variational model for the ice-water interface and compute the free energy barrier as a function of the supercooling, the AFP footprint size, and the distance to neighboring AFPs on the ice surface. We then use a stochastic survival probability model to predict the TH as a function of ice/water properties, AFP size, and AFP coverage. Remarkably, our TH predictions (with no adjustable parameters) approximately agree with those in experiments.