Modelling the influence of antifreeze proteins on three-dimensional ice crystal melt shapes using a geometric approach

The melting of pure axisymmetric ice crystals has been described previously by us within the framework of so-called geometric crystal growth. Non-equilibrium ice crystal shapes evolving in the presence of hyperactive antifreeze proteins (hypAFPs) are experimentally observed to assume ellipsoidal geometries (‘lemon’ or ‘rice’ shapes). To analyse such shapes, we harness the underlying symmetry of hexagonal ice Ih and extend two-dimensional geometric models to three-dimensions to reproduce the experimental dissolution process. The geometrical model developed will be useful as a quantitative test of the mechanisms of interaction between hypAFPs and ice.