Theory of simple biochemical "shape recognition" via diffusion from activator coated nanoshapes

Inspired by recent experiments, we model the shape sensitivity, via a typical threshold initiation response, of an underlying complex biochemical reaction network to activator coated nanoshapes. Our theory re-emphasizes that shape effects can be vitally important for the onset of functional behavior in nanopatches and nanoparticles. For certain critical or particular shapes, activator coated nanoshapes do not evoke a threshold response in a complex biochemical network setting, while for different critical or specific shapes, the threshold response is rapidly achieved. The model thus provides a general theoretical understanding for how activator coated nanoshapes can enable a chemical system to perform simple "shape recognition," with an associated "all or nothing" response. The novel and interesting cases of the chemical response due to a nanoshape that shrinks with time is additionally considered, as well as activator coated nanospheres. Possible important applications of this work include the initiation of blood clotting by nanoshapes, nanoshape effects in nanocatalysis, physiological toxicity to nanoparticles, as well as nanoshapes in nanomedicine, drug delivery, and T cell immunological response. The aim of the theory presented here is that it inspires further experimentation on simple biochemical shape recognition via diffusion from activator coated nanoshapes.