According to the properties of type I antifreeze protein (AFPI) within the interfacial region of ice and water, the theoretical model of the large ligands binding on one-dimensional homogeneous lattice have been extended to two-dimensional lattice-like surface (ice surface). By using of this two-dimensional model, the fractions of the ice crystal surface covered by four AFPI variants that have different intrinsic binding constants and sizes are calculated, respectively. The thermal hysteresis activities of these proteins are obtained. The theoretical results are agreement with the reported experimental data. (c) 2006 Elsevier B.V. All rights reserved.