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We consider a coupled bulk-surface system of partial differential equationswith nonlinear coupling modelling receptor-ligand dynamics. The model arises asa simplification of a mathematical model for the reaction between cell surfaceresident receptors and ligands present in the extra-cellular medium. We provethe existence and uniqueness of solutions. We also consider a number ofbiologically relevant asymptotic limits of the model. We prove convergence tolimiting problems which take the form of free boundary problems posed on thecell surface. We also report on numerical simulations illustrating convergenceto one of the limiting problems as well as the spatio-temporal distributions ofthe receptors and ligands in a realistic geometry.

Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics