  A quantitative model of the mobility of functionalized particles at the
interface is pivotal to understanding important systems in biology and
nanotechnology. In this work, we investigate the emerging dynamics of particles
anchored through ligand-receptor bridges to functionalized surfaces. We
consider systems with reversible bridges in which ligand-receptor pairs
bind/unbind with finite reaction rates. For a given set of bridges, the
particle can explore a tiny fraction of the surface as the extensivity of the
bridges is finite. We show how at time scales longer than the bridges'
lifetime, the averaged position of the particle diffuses away from its initial
value. We distill our findings into two analytic equations for the sliding
diffusion constant of particles carrying mobile and fixed ligands. We
quantitatively validate our theoretical predictions using reaction-diffusion
simulations. Our results, along with recent literature, will allow inferring
the microscopic parameters at play in complex biological systems from
experimental trajectories.
