  Multivalent particles, i.e. microscopic constructs having multiple ligands,
can be used to target surfaces selectively depending on their receptor density.
Typically, there is a sharp onset of multivalent binding as the receptor
density exceeds a given threshold. However, the opposite case, selectively
binding to surfaces with a receptor density below a given threshold, is much
harder. Here, we present a simple strategy for selectively targeting a surface
with a low density of receptors, within a system also having a surface with a
higher density of the same receptors. Our strategy exploits competitive
adsorption of two species. The first species, called "guards", are
receptor-sized monovalent particles designed to occupy the high-density surface
at equilibrium, while the second multivalent "attacker" species outcompetes the
guards for binding onto the low-density surface. Surprisingly, the recipe for
attackers and guards yields more selective binding with stronger
ligand-receptor association constants, in contrast to standard multivalency. We
derive explicit expressions for the attacker and guard molecular design
parameters and concentrations, optimised within bounds of what is
experimentally accessible, thereby facilitating implementation of the proposed
approach.
