Enhanced reaction kinetics in biological cells

The cell cytoskeleton is a striking example of an active medium driven out-of-equilibrium by ATP hydrolysis. Such activity has been shown to have a spectacular impact on the mechanical and rheological properties of the cellular medium, as well as on its transport properties: a generic tracer particle freely diffuses as in a standard equilibrium medium, but also intermittently binds with random interaction times to motor proteins, which perform active ballistic excursions along cytoskeletal filaments. Here, we propose an analytical model of transport-limited reactions in active media, and show quantitatively how active transport can enhance reactivity for large enough tracers such as vesicles. We derive analytically the average interaction time with motor proteins that optimizes the reaction rate, and reveal remarkable universal features of the optimal configuration. We discuss why active transport may be beneficial in various biological examples: cell cytoskeleton, membranes and lamellipodia, and tubular structures such asaxons.