title: Theory of diffusion-influenced reactions in complex geometries.
abstract: Chemical transformations involving the diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced reactions" (DIR). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DIRs, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory that is able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DIR reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases.
authors.affiliation: Università degli Studi di Firenze, Dipartimento di Fisica e Astronomia and CSDC, via G. Sansone 1, IT-50019 Sesto Fiorentino, Firenze, Italia. Francesco.Piazza@gmail.com.
authors.forename: Marta
authors.initials: M
authors.lastname: Galanti
authors.forename: Duccio
authors.initials: D
authors.lastname: Fanelli
authors.forename: Sergey D
authors.initials: SD
authors.lastname: Traytak
authors.forename: Francesco
authors.initials: F
authors.lastname: Piazza