  Multivalent particles competing for binding on the same surface can exhibit
switch-like behaviour, depending on the concentration of receptors on the
surface. When the receptor concentration is low, energy dominates the free
energy of binding, and particles having a small number of strongly-binding
ligands preferentially bind to the surface. At higher receptor concentrations,
multivalent effects become significant, and entropy dominates the binding free
energy; particles having many weakly-binding ligands preferentially bind to the
surface. Between these two regimes there is a "switch-point", at which the
surface binds the two species of particles equally strongly. We demonstrate
that a simple theory can account for this switch-like behaviour and present
numerical calculations that support the theoretical predictions. We argue that
binding selectivity based on receptor density, rather than identity, may have
practical applications.
