Reaction kinetics in active media

Reactants in biological cells can either freely diffuse or bind to molecular motors which perform ballistic active motion along the cytoskeletal filaments. The transport process is therefore intermittent since it alternates diffusive reactive phases and ballistic non-reactive phases. Here we present an overview of recent results (Bénichou et al 2006 Phys. Rev. E 74 020102, Loverdo et al 2008 Nat. Phys. 4 134) which enables us to determine the kinetic constant of reactions limited by such intermittent transport. We address the question of optimizing the reaction rate as a function of the mean durations of each phase. To answer such questions, we calculate explicitly the mean first-passage time to the target. We conclude that intermittent transport can maximize the reaction rate, and that there are optimal durations of the two phases. We studied this model in one, two and three dimensions. All these cases are relevant to reactivity in biological cells. Indeed, structures such as dendrites can be considered as one-dimensional, membranes as two-dimensional, and bulk cytoplasm as three-dimensional. We show that the dependence on the target density is important in the one-dimensional case, weak in the two-dimensional case, and disappears in the three-dimensional case. Our results are robust, as different descriptions of the reactive phase lead to the same optimal duration of the ballistic phase.