Monte Carlo Investigation of Diffusion of Receptors and Ligands that Bind Across Opposing Surfaces

Studies of receptor diffusion on a cell surface show a variety of behaviors, such as diffusive, sub-diffusive, or super-diffusive motion. However, most studies to date focus on receptor molecules diffusing on a single cell surface. We have previously studied receptor diffusion to probe the molecular mechanism of receptor clustering at the cell–cell junction between two opposing cell surfaces. Here, we characterize the diffusion of receptors and ligands that bind to each other across two opposing cell surfaces, as in cell–cell and cell–bilayer interactions. We use a Monte Carlo method, where receptors and ligands are simulated as independent agents that bind and diffuse probabilistically. We vary receptor–ligand binding affinity and plot the molecule-averaged mean square displacement (MSD) of ligand molecules as a function of time. Our results show that MSD plots are qualitatively different for flat and curved interfaces, as well as between the cases of presence and absence of directed transport of receptor–ligand complexes toward a specific location on the interface. Receptor–ligand binding across two opposing surfaces leads to transient sub-diffusive motion at early times provided the interface is flat. This effect is entirely absent if the interface is curved, however, in this instance we observe sub-diffusive motion. In addition, a decrease in the equilibrium value of the MSD occurs as affinity increases, something which is absent for a flat interface. In the presence of directed transport of receptor–ligand complexes, we observe super-diffusive motion at early times for a flat interface. Super-diffusive motion is absent for a curved interface, however, in this case we observe a transient decrease in MSD with time prior to equilibration for high-affinity values.