  Targeted drug delivery relies on two physical processes: the selective
binding of a therapeutic particle to receptors on a specific cell membrane,
followed by transport of the particle across the membrane. In this article, we
address some of the challenges in controlling the thermodynamics and dynamics
of these two processes by combining a simple experimental system with a
statistical mechanical model. Specifically, we characterize and model
multivalent ligand-receptor binding between colloidal particles and fluid lipid
bilayers, as well as the surface mobility of membrane-bound particles. We show
that the mobility of the receptors within the fluid membrane is key to both the
thermodynamics and dynamics of binding. First, we find that the
particle-membrane binding free energy -- or avidity -- is a strongly nonlinear
function of the ligand-receptor affinity. We attribute the nonlinearity to a
combination of multivalency and recruitment of fluid receptors to the binding
site. Our results also suggest that partial wrapping of the bound particles by
the membrane enhances avidity further. Second, we demonstrate that the lateral
mobility of membrane-bound particles is also strongly influenced by the
recruitment of receptors. Specifically, we find that the lateral diffusion
coefficient of a membrane-bound particle is dominated by the hydrodynamic drag
against the aggregate of receptors within the membrane. These results provide
one of the first direct validations of the working theoretical framework for
multivalent interactions. They also highlight that the fluidity and elasticity
of the membrane are as important as the ligand-receptor affinity in determining
the binding and transport of small particles attached to membranes.
