Collision-mediated Transfer Kinetics of Cargo Items among Mobile Nanocarriers

Micelles, liposomes, microgels, dendrimers, and nanoparticles represent nanocarriers that deliver cargo items–often drug molecules to a target. We calculate the kinetics of collision-mediated transfer of cargo items within ensembles of chemically distinct mobile nanocarriers in the Gaussian regime. To this end, the relevant rate equations for collision-mediated transfer of cargo items are expressed in the continuum limit as a set of Fokker-Planck equations and solved analytically. The solutions fully describe the time evolution of an arbitrary initial distribution of the cargo items among the nanocarriers toward equilibrium. In the present work, we focus on analyzing the eigenvalues of the rate matrix, including their transition from real values to pairs of complex conjugate values. We characterize the physical implications of the transition in terms of the detailed distributions of cargo items in each nanocarrier population. The simplest case exhibiting a transition is that of three chemically distinct nanocarrier components, which we discuss comprehensively.