Modeling the binding of cholera toxin to a lipid membrane by a non-additive two-dimensional hard-disk model

A coupled two-layer hard-disk model in two dimensions inspired by the interactions of mixtures of different lipids in the outer bilayer leaflet was derived. It is effectively a non-additive mixture of hard disks. A gas and a crystal phase are observed. The recognition and binding of pathogenic cholera toxin are modeled by fixing lipid-binding sites in space in pentagonal geometries constrained by the protein. At constant pressure, this positional constraint leads to an increase in the area per molecule as the lipid-packing structure is distorted. This distortion increases with increasing density or pressure. Variations of the basic model are discussed. We find that the overall area per molecule scales with the area per molecule of the majority component.