A Theoretical Model Of Antifreeze Protein Irreversible Ninding To Ice Surface

Antifreeze proteins (AFPs) are a subset of proteins that can control the growth of ice crystal. AFPs adsorb on the surfaces of ice crystals and decrease the freezing point of ice crystal with non-colligative effect but have no influence on the melting point. Thereby creating a gap (thermal hysteresis or TH) between the melting point and the nonequilibrium freezing point in which ice growth is arrested.In the past, we think the binding of AFPs on the surface of ice crystals is a reversible process. But microfluidic experiments have provided direct evidence that the binding of hyperactive TmAFP molecules to ice crystals is practically irreversible. Although the dependence of TH activity on the AFP concentration has been studied extensively, the time-dependent TH activities dependence of this process still remains unclear. Some experimental studies for dependence of TH activities on time of moderate AFPs have been reported, and a few recent studies of hypAFPs are available. And they did not give a theoretical explain on the mechanisms of the time-dependent TH activity of AFPs.Based on the theory of "adsorption-inhibition", according to the dynamic adsorption process of AFPs on the ice crystals surface, we extend the theoretical model for irreversible binding of ligands of arbitrary length to one-dimensional lattices to a system that large ligands (TmAFPs) binding on two-dimensional lattice-like surface (ice surface). The model is derived in terms of ligand site size and intrinsic binding rate constant. By using of this two-dimensional model, the time-dependent fractions of ice crystal surface covered by TmAFPs that at different concentration are calculated, respectively. And the thermal hysteresis activity of these TmAFPs are obtained quantitatively. In particular, this model is dynamically able to explain the change of time-dependent TH activities observed experimentally when the concentration of the TmAFPs is changed.The theoretical conclusions are consistent with the reported experimental observations. Our results suggest that the coverage of TmAFPs on the ice surface increases with a slow and progressive manner. And the exposure time is an equally necessary condition for their TH activity in addition to TmAFP’s recognition of the ice surface with affinity and specificity. Therefore, the two-dimensional irreversible theoretical model adsorption established contribute to our understanding of the mechanism of AFPs irreversible binding to ice surface.