  Chemical reactions involving diffusion of reactants and subsequent chemical
fixation steps are generally termed "diffusion-influenced" (DI). 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 DI reactions, and is therefore a prime design parameter. Yet,
it is a formidable challenge to build a comprehensive theory 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
DI 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.
