Antifreeze Proteins Bind Irreversibly to Ice, so Why Does Thermal Hysteresis Depend on Bulk Concentration?

Antifreeze proteins (AFPs) on ice surfaces create pinning sites which resist ice growth. The maximum degree of supercooling to which an AFP can prevent ice growth is its thermal hysteresis (TH). Survival probabilities based on a model for engulfment kinetics explain how TH depends on AFP surface coverage, AFP size, ice surface area, and cooling rates. However, they do not explain the dependence of TH on bulk AFP concentration, an effect seen in many experiments. Here we reassess TH data in terms of total time-of-exposure, t_exp (including protocol variables like incubation time and cooling rate), which together with the bulk AFP concentration (C_bulk) influences the surface coverage. For data sets on two different AFPs with TH measured in two different ways, the product C_bulkt_exp, suggested by a simple model of adsorption, is a better predictor of TH than bulk concentration or exposure time alone. Our results suggest that effects of bulk concentration on TH are indirect, with bulk concentration influencing surface coverage, and surface coverage having a direct influence on TH.