Fly in the sky or creep on the earth:
What is the optimal search strategy?

by D. S. Grebenkov

We present an exact calculation of the mean first-passage time
to a small target on the surface of a 2D or 3D spherical domain,
for a molecule performing surface-mediated diffusion. This
minimal model of interfacial reactions, which explicitly takes
into account the combination of surface and bulk diffusion, shows
the importance of correlations induced by the coupling of the
switching dynamics to the geometry of the confinement, ignored
so far. Our results show that, in the context of interfacial
systems in confinement, the reaction time can be minimized as
a function of the desorption rate from the surface, which puts
forward a general mechanism of enhancement and regulation of
chemical and biological reactivity.