  The dynamics of particles interacting by key-lock binding of attached
biomolecules are studied theoretically. Examples of such systems include
DNA-functionalized colloids as well as nanoparticles grafted with antibodies to
cell membrane proteins. Depending on the coverage of the functional groups, we
predict two distinct regimes separated by a percolation transition. In the
localized regime at low coverage, the system exhibits a broad, power law like
distribution of particle departure times. At higher coverage, there is an
interplay between departure dynamics and particle diffusion. This interplay
leads to a sharp increase of the departure times, a phenomenon qualitatively
similar to aging in glassy systems. This diffusive regime is analogous to
dispersive transport in disordered semiconductors: depending on the interaction
parameters, the diffusion behavior ranges from standard diffusion to anomalous,
subdiffusive behavior. The connection to recent experiments and implications
for future studies are discussed.

Soft Condensed Matter;Statistical Mechanics