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. Diffusion-influenced reactions (DIR) are ubiquitous in many contexts in physics, chemistry and biology [1,2] and keep on sparking intense theoretical and computational activity in many fields [3][4][5][6][7][8][9][10][11]. Modern examples of emerging nanotechnologies that rely on controlled alterations of diffusion and reaction pathways in DIRs include different sorts of chemical and biochemical catalysis involving complex nano-reactors [12,13], nanopore-based sequencing engines [14] and morphology control and surface functionalization of inorganic-based delivery vehicles for controlled intracellular drug release [15,16].However, while the mathematical foundations for the description of such problems have been laid nearly a century ago [17], many present-day problems of the utmost importance at both the fundamental and applied level are still challenging. Notably, arduous difficulties arise in the quantification of the important role played by the environment's geometry (obstacles, compartmentalization) [18] and distributed reactivity (patterns of competitive reaction targets or traps) in coupling transport and reaction pathways in many natural and artificial (bio)chemical reactions [1,19,20].A formidable challenge in modeling environmentrelated effects on chemical reactions is represented by the intrinsic many-body nature of the problem. This is brought about essentially by two basic features, common to virtually all realistic situations, namely (i) finite density of reactants and other inert species (in biology also referred to as macromolecular crowding [21,22]) and (ii) confining geometry of natural or artificial reaction domains in 3D space. In general, the presence of multiple reactive and non-reactive particles/boundaries cannot be neglected in the study of (bio)chemical reactions occurring in real milieux, where the geometrical compactness of the environment may have profound effects, such as first-passage times that are non-trivially influenced by the starti...

Antibodies are large, extremely flexible molecules, whose internal dynamics is certainly key to their astounding ability to bind antigens of all sizes, from small hormones to giant viruses. In this paper, we build a shape-based coarse-grained model of IgG molecules and show that it can be used to generate 3D conformations in agreement with single-molecule Cryo-Electron Tomography data. Furthermore, we elaborate a theoretical model that can be solved exactly to compute the binding rate constant of a small antigen to an IgG in a prescribed 3D conformation. Our model shows that the antigen binding process is tightly related to the internal dynamics of the IgG. Our findings pave the way for further investigation of the subtle connection between the dynamics and the function of large, flexible multi-valent molecular machines.