Diffusion Attachment Model for Long Helical Antifreeze Proteins to Ice

Some of the most potent antifreeze proteins (AFPs) are approximately rigid helical structures that bind with one side in contact with the ice surface at specific orientations. These AFPs take random orientations in solution; however, most orientations become sterically inaccessible as the AFP approaches the ice surface. The effect of these inaccessible orientations on the rate of adsorption of AFP to ice has never been explored. Here, we present a diffusion-controlled theory of adsorption kinetics that accounts for these orientational restrictions to predict a rate constant for adsorption (k_on, in m/s) as a function of the length and width of the AFP molecules. We find that k_on decreases with length and diameter of the AFP and is almost proportional to the inverse of the area of the binding surface. We demonstrate that the restricted orientations create an entropic barrier to AFP adsorption, which we compute to be approximately 7 k_BT for most AFPs and up to 9 k_BT for Maxi, the largest known AFP. We compare the entropic resistance 1/k_on to resistances for diffusion through boundary layers and across typical distances in the extracellular matrix and find that these entropic and diffusion resistances could become comparable in the small confined spaces of biological environments.