Modified Langmuir isotherm for a two-domain adsorbate: derivation and application to antifreeze proteins

Many organisms are exposed to subzero temperatures in nature and can survive these temperatures by the effect of antifreeze proteins (AFPs), which inhibit ice crystal growth and change the morphology of ice crystals. Although the effects of these proteins, such as recrystallization inhibition, ice growth inhibition, and crystal habit changes, are known, a conclusive description of the protein-ice crystal interaction including interaction energy, surface coverage, and lifetime of adsorbate has been elusive. In this study, we determine the binding equilibrium constant for a type III fish antifreeze protein and the relationship between thermal hysteresis and surface coverage for this protein. This is possible using experimental data from a two-domain antifreeze protein and its related single domain protein. The classical Langmuir isotherm is used to describe the equilibrium exchange of the single domain type III AFP molecules at the ice crystal surface, while a modification of the Langmuir isotherm is derived to describe the adsorption of the two-domain AFP. Because the protein adsorption is governed by different isotherm relationships, there are two independent data sets allowing the determination of the two unknowns of surface coverage and binding energy. The data yield an equilibrium binding constant of 1.9 mM(-1) for the type III AFP-ice interaction. The analysis results in a relationship between surface coverage and thermal hysteresis, as well as kinetic equations of the adsorption of the proteins onto the ice surface.