Collision-mediated transfer kinetics of cargo among mobile nanocarriers

Micelles, liposomes, microgels, dendrimers, macrocyclic host molecules, and nanoparticles represent nanocarriers used to transfer cargo, such as drug molecules, among each other and to target sites. We calculate the kinetics of collision-mediated transfer of cargo within ensembles of chemically distinct mobile nanocarriers that each hosts noninteracting cargo items on discrete and identical sites. Rate equations for collision-mediated transfer of cargo are expressed in the Gaussian limit as a set of Fokker-Planck equations and solved in the limit of low occupation. The results are analytic expressions for the detailed cargo distributions of each carrier type as a function of time, from an arbitrary initial apportionment to a set of Gaussians in equilibrium.