Sticky diffusion: How to achieve complex motion with random sticky feet ?

Beating equilibrium diffusion is a paradigm challenge that biological or artificial systems of small particles have to face to achieve complex functions. Some cells (like leucocytes) use ligand-receptor contacts (sticky feet) to crawl and roll along vessels. Sticky DNA (another type of sticky feet) is coated on colloids to design programmable interactions and long-range assembly features. The dynamics of such sticky motion are complex as sticky events (attaching/detaching) often occur on very short time scales that affect the overall motion of the particle on much longer time scales, and makes predictions challenging. Here we present analytical predictions in several cases (with different geometries of sticky feet). We rationalize what parameters control diffusion and how they can be compared to existing systems. We investigate furthermore how complex motion like rolling may be favored compared to lateral motion.