Diffusion Attachment Model for Long Helical Antifreeze Proteins to Ice

Accumulation of Antifreeze Proteins on Ice Is Determined by Adsorption

Antifreeze proteins (AFPs) facilitate the survival of diverse organisms in frigid environments by adsorbing to ice crystals and suppressing their growth. The rate of AFP accumulation on ice is determined by an interplay between AFP diffusion from the bulk solution to the ice-water interface and the subsequent adsorption of AFPs to the interface. To interrogate the relative importance of these two processes, here, we combine nonequilibrium fluorescence experiments with a reaction-diffusion model. We find that as diverse AFPs accumulate on ice, their concentration in the aqueous solution does not develop a gradient but remains equal to its bulk concentration throughout our experiments. These findings lead us to conclude that AFP accumulation on ice crystals, which are smaller than 100 μm in radius, is not limited by the diffusion of AFPs, but by the kinetics of AFP adsorption. Our results imply that mass transport limitations do not hinder AFPs from performing their biological function.

Characterizing Surface Ice-Philicity Using Molecular Simulations and Enhanced Sampling

The formation of ice, which plays an important role in diverse contexts ranging from cryopreservation to atmospheric science, is often mediated by solid surfaces. Although surfaces that interact favorably with ice (relative to liquid water) can facilitate ice formation by lowering nucleation barriers, the molecular characteristics that confer icephilicity to a surface are complex and incompletely understood. To address this challenge, here we introduce a robust and computationally efficient method for characterizing surface ice-philicity that combines molecular simulations and enhanced sampling techniques to quantify the free energetic cost of increasing surface-ice contact at the expense of surface-water contact. Using this method to characterize the ice-philicity of a family of model surfaces that are lattice matched with ice but vary in their polarity, we find that the nonpolar surfaces are moderately ice-phobic, whereas the polar surfaces are highly ice-philic. In contrast, for surfaces that display no complementarity to the ice lattice, we find that ice-philicity is independent of surface polarity and that both nonpolar and polar surfaces are moderately ice-phobic. Our work thus provides a prescription for quantitatively characterizing surface ice-philicity and sheds light on how ice-philicity is influenced by lattice matching and polarity.

Engulfment Avalanches and Thermal Hysteresis for Antifreeze Proteins on Supercooled Ice

Antifreeze proteins (AFPs) bind to the ice-water surface and prevent ice growth at temperatures below 0 °C through a Gibbs-Thomson effect. Each adsorbed AFP creates a metastable depression on the surface that locally resists ice growth, until ice engulfs the AFP. We recently predicted the susceptibility to engulfment as a function of AFP size, distance between AFPs, and supercooling [ J. Chem. Phys. 2023, 158, 094501]. For an ensemble of AFPs adsorbed on the ice surface, the most isolated AFPs are the most susceptible, and when an isolated AFP gets engulfed, its former neighbors become more isolated and more susceptible to engulfment. Thus, an initial engulfment event can trigger an avalanche of subsequent engulfment events, leading to a sudden surge of unrestrained ice growth. This work develops a model to predict the supercooling at which the first engulfment event will occur for an ensemble of randomly distributed AFP pinning sites on an ice surface. Specifically, we formulate an inhomogeneous survival probability that accounts for the AFP coverage, the distribution of AFP neighbor distances, the resulting ensemble of engulfment rates, the ice surface area, and the cooling rate. We use the model to predict thermal hysteresis trends and compare with experimental data.

Oriented attachment kinetics for rod-like particles at a flat surface: Buffon's needle at the nanoscale

The adsorption of large rod-like molecules or crystallites on a flat crystal face, similar to Buffon's needle, requires the rods to "land," with their binding sites in precise orientational alignment with matching sites on the surface. An example is provided by long, helical antifreeze proteins (AFPs), which bind at specific facets and orientations on the ice surface. The alignment constraint for adsorption, in combination with the loss in orientational freedom as the molecule diffuses toward the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule, nor explicitly enforce orientational constraints for adsorption. Here, we develop a diffusion-controlled adsorption theory for AFP molecules binding at specific orientations to flat ice surfaces. We formulate the diffusion equation with relevant boundary conditions and present analytical solutions to the attachment rate constant. The resulting rate constant is a function of the length and aspect ratio of the AFP, the distance threshold associated with binding, and solvent conditions such as temperature and viscosity. These results and methods of calculation may also be useful for predicting the kinetics of crystal growth through oriented attachment.