Thermal hysteresis activity of antifreeze proteins: A model based on fractional statistics theory of adsorption

Antifreeze proteins (AFPs) adsorb to the surface of embryonic ice crystals to prevent their growth. The protein-ice adsorption lowers the freezing point of the solution. Then, a thermal hysteresis can be defined as the difference between the melting and freezing temperatures. This quantity is a measure of the antifreeze protein activity. In this sense, there exists evidence that the antifreeze activity enhances with increasing the area/length of the ice-binding sites. In order to interpret this thermal hysteresis behavior, we introduce a two-dimensional adsorption model based on fractional statistics theory. The analytical expressions are obtained in terms of an exclusion parameter, which depend on the structure of the protein and area of the ice-binding sites. By using the model, thermal hysteresis activity is calculated for AFPs of different size, shape and number of active sites. The theoretical results show a good qualitative agreement with reported experimental data in the literature. •A new approach to model thermal hysteresis (TH) activity of antifreeze protein.•The formalism is based on fractional statistics theory of adsorption.•An explicit dependence of the TH activity on the binding sites area is obtained.•The theory is applied to experimental data of binding proteins of different sizes.•TH activity increases with increasing the number and area of the ice-binding sites.