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Diffusion to capture is an ubiquitous phenomenon in many fields in biologyand physical chemistry, with implications as diverse as ligand-receptor bindingon eukaryotic and bacterial cells, nutrient uptake by colonies of unicellularorganisms and the functioning of complex core-shell nanoreactors. Whenever manyboundaries compete for the same diffusing molecules, they inevitably shield avariable part of the molecular flux from each other. This gives rise to theso-called diffusive interactions (DI), which can reduce substantially theinflux to a collection of reactive boundaries depending chiefly on theirgeometrical configuration. In this review we provide a pedagogical discussionof the main mathematical aspects underlying a rigorous account of DIs. Startingfrom a striking and deep result on the mean-field description of ligand bindingto a receptor-covered cell, we develop little by little a rigorous mathematicaldescription of DIs in the stationary case through the use of translationaladdition theorems for spherical harmonics. We provide several enlighteningillustrations of this powerful mathematical theory, including diffusion tocapture to ensembles of reactive boundaries within a spherical cavity.

Diffusion to capture and the concept of diffusive interactions