  Nanoparticles with multiple ligands have been proposed for use in
nanomedicine. The multiple targeting ligands on each nanoparticle can bind to
several locations on a cell surface facilitating both drug targeting and
uptake. Experiments show that the distribution of conjugated ligands is
unexpectedly broad, and the desorption rate appears to depends exponentially
upon the mean number of attached ligands. These two findings are explained with
a model in which ligands conjugate to the nanoparticle with a positive
cooperativity of $\approx 4kT$, and that nanoparticles bound to a surface by
multiple bonds are permanently affixed. This drives new analysis of the data,
which confirms that there is only one time constant for desorption, that of a
nanoparticle bound to the surface by a single bond.
