  The cell cytoskeleton is a striking example of "active" medium driven
out-of-equilibrium by ATP hydrolysis. Such activity has been shown recently 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 for the first time an analytical model of transport limited reactions
in active media, and show quantitatively how active transport can enhance
reactivity for large enough tracers like vesicles. We derive analytically the
average interaction time with motor proteins which 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 like
axons.
