Engulfment Avalanches and Thermal Hysteresis for Antifreeze Proteins on Supercooled Ice

Antifreeze proteins (AFPs) bind to the ice-water surface and prevent ice growth at temperatures below 0 °C through a Gibbs-Thomson effect. Each adsorbed AFP creates a metastable depression on the surface that locally resists ice growth, until ice engulfs the AFP. We recently predicted the susceptibility to engulfment as a function of AFP size, distance between AFPs, and supercooling [ J. Chem. Phys. 2023, 158, 094501 ]. For an ensemble of AFPs adsorbed on the ice surface, the most isolated AFPs are the most susceptible, and when an isolated AFP gets engulfed, its former neighbors become more isolated and more susceptible to engulfment. Thus, an initial engulfment event can trigger an avalanche of subsequent engulfment events, leading to a sudden surge of unrestrained ice growth. This work develops a model to predict the supercooling at which the first engulfment event will occur for an ensemble of randomly distributed AFP pinning sites on an ice surface. Specifically, we formulate an inhomogeneous survival probability that accounts for the AFP coverage, the distribution of AFP neighbor distances, the resulting ensemble of engulfment rates, the ice surface area, and the cooling rate. We use the model to predict thermal hysteresis trends and compare with experimental data.