  Much work has studied effective interactions between micron-sized particles
carrying linkers forming reversible, inter-particle linkages. These studies
allowed understanding the equilibrium properties of colloids interacting
through ligand-receptor interactions. Nevertheless, understanding the kinetics
of multivalent interactions remains an open problem. Here, we study how
molecular details of the linkers, such as the reaction rates at which
inter-particle linkages form/break, affect the relative dynamics of pairs of
cross-linked colloids. Using a simulation method tracking single
binding/unbinding events between complementary linkers, we rationalize recent
experiments and prove that particles' interfaces can move across each other
while being cross-linked. We clarify how, starting from diffusing colloids, the
dynamics become arrested when increasing the number of inter-particle linkages
or decreasing the reaction rates. Before getting arrested, particles diffuse
through rolling motion. The ability to detect rolling motion will be useful to
shed new light on host-pathogen interactions.
