  Multivalent particles have the ability to form multiple bonds to a substrate.
Hence, a multivalent interaction can be strong, even if the individual bonds
are weak. However, much more interestingly, multivalency greatly increases the
sensitivity of the particle-substrate interaction to external conditions,
resulting in an ultra-sensitive and highly non-linear dependence of the binding
strength on parameters such as temperature, pH or receptor concentration.
  In this chapter we focus on super-selectivity: the high sensitivity of the
strength of multivalent binding to the number of accessible binding sites on
the target surface. For example, the docking of a multivalent particle on a
cell-surface can be very sensitive (super-selective) to the concentration of
the receptors to which the multiple ligands can bind.
  We present a theoretical analysis of systems of multivalent particles and
describe the mechanism by which multivalency leads to super-selectivity. We
introduce a simple analytical model that allows us to predict the overall
strength of interactions based on physiochemical characteristics of multivalent
binders. Finally, we formulate a set of simple design rules for multivalent
interactions that yield optimal selectivity.
